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The generalization for interval fuzzy set name as neutrosophic set employed to construct a measurable space in this work. The measurable space with respect to a ring of sets that is closed under difference and union, is studied. The objective of this study is to extend the notion of a ring of sets by using neutrosophic sets. Neutrosophic set concept has gained popularity in various fields of mathematics, probability, and other sciences due to its many uses, especially when dealing with uncertainties. Several different properties of neutrosophic ring are studied. Examples and characterizations to the proposed extension are given. [ABSTRACT FROM AUTHOR]

A rough set is an approximation of a subset of a universe. Rough sets are mainly used in decision-making when the given data is uncertain. Rough set theory is a groundbreaking approach that provides a formal framework for extracting facts from imperfect data and helps us classify objects based on their similarities. Developing an algebraic structure for rough sets facilitates a detailed study of the settheoretic properties. In this paper, we consider the universe as a ring and obtain rough set results. We consider a new equivalence relation on a ring R whose equivalence classes form a partition of R. Then, we define upper and lower approximations of a subset of a ring R with respect to the given equivalence relation. Subsequently, we prove related results on these approximations and are illustrated with suitable examples. In addition, we obtain the relationship between the upper and lower approximations defined in this paper and the ones defined earlier. [ABSTRACT FROM AUTHOR]

Introduction: In this review article, we aim to illustratively address abnormal and normal courses of Plastibell (a system designed to remove the correct amount of skin) circumcision. We searched 2 target databases, PubMed and Embase, for Plastibell ring circumcision and recruited photos from circumcised children with plasticbell rings. The ordinary postprocedure healing course may resemble abnormal situations such as infection and dehiscence. Conversely, adverse events are rarely noticed by parents. Thus, medical attention is sought when it is not needed and omitted when the specialist may require an intervention. Conclusion: Providing a pamphlet illustrating standard normal and abnormal features of plastic bell ring circumcision will decrease family stress, emergency referrals, and preventable complications in this standard procedure. [ABSTRACT FROM AUTHOR]

A commutative ring over a graph was first studied by Beck in 1988. The properties of zero-divisor graphs of commutative and non-commutative rings were then studied extensively. The commutative ring over graph is also widely used in robotics, communication theory, and elliptic curve cryptography. In this paper, we derive a few degree-based topological expressions namely, the first Zagreb index and the forgotten index of zero-divisor graphs of Z p n , Z q × Z p n and Z q 2 × Z p n where p and q are primes. The numerical expression of the zero-divisor graphs is analysed and compared the indices graphically and numerically. [ABSTRACT FROM AUTHOR]

AbstractIn this article, we firstly investigate some properties of one-sided core inverses. Particularly, new characterizations for left core inverses are given in terms of projections and units. Also, we introduced a new one-side generalized inverse which is called one-sided EP-inverse. Given a∈R, we say that a is left EP-invertible if there exists an x∈R such that axa=a, (ax)∗=ax, xa2=a and x2a=x. Several characterizations of the left EP-invertibility are derived. For instance, it is proved that a is left EP-invertible if and only if there exists an x∈R such that axa=a, (ax)∗=ax and x2a=x. Moreover, it is also proven that a is left EP-invertible if and only if a∈a∗R∩Ra∗a. Finally, we introduce the right EP-invertibility and obtain some results dual to those on the (right) EP-invertibility. [ABSTRACT FROM AUTHOR]

AbstractThis article is dedicated to the free vibrational analysis of a laminated three-phase polymer/GNP/fiber conical shell stiffened with a desired number of intermediate rings. The shell is fabricated from a feeble but low-density polymeric matrix enriched simultaneously with graphene nanoplatelets (GNPs) and aligned fibers. It is assumed that the volume fractions of the matrix, fibers, and GNPs vary along the thickness direction. The laminated shell is modeled according to Murakami’s zig-zag theory and the intermediate rings are considered as rigid structures. The effective elastic constants and the density of the structure are calculated via the Halpin-Tsai model, the rule of mixture, and micromechanical equations. The governing equations, boundary conditions, and compatibility conditions imposed by the ring supports are derived using Hamilton’s principle. A semi-analytical solution is presented to calculate the natural frequencies for various boundary conditions. This solution includes an analytical one in the circumferential direction followed by a numerical solution in the meridional direction. The relationships between the natural frequencies and several parameters are discussed in detail including the boundary conditions, number and location of the rings, weight fractions and dispersion patterns of GNPs and fibers. It is observed that to achieve higher natural frequencies, it is more helpful to distribute the GNPs and fibers far from the middle surface and near the inner and outer surfaces of the shell, especially the inner one. [ABSTRACT FROM AUTHOR]

This paper aims to establish the following: Let $ \Omega $ be a ring that satisfies some conditions and has an idempotent element $ f\neq 0, 1 $. We intend to show that if $ G $ is any suitable multiplicative generalized CE-derivation of $ \Omega $, then $ G $ is a centrally extended additive.

Despite great societal efforts promoting female autonomy, Sweden still faces unmet contraceptive needs, with abortion rates being the highest in the Nordic countries. In this commentary, we discuss using non‐daily contraception options to combat these unmet needs. Non‐daily methods include transdermal (i.e., patch), ring, injectables, and long‐acting reversible contraception (LARC). Numerous studies have revealed that users prefer non‐daily methods, and studies implementing structured counseling have revealed an increase in non‐daily methods. Relative to LARC, the patch and the ring are non‐daily parenteral methods that offer the possibility for self‐management. Ultimately, client‐centered counseling and shared decision‐making are crucial for increasing awareness of all methods and enhancing method utilization and adherence. Finally, dispelling myths surrounding reversible hormonal contraception is essential for empowering women to make informed choices and improving overall reproductive health outcomes. [ABSTRACT FROM AUTHOR]

We present necessary and sufficient conditions under which the sum of two group invertible elements in a ring is group invertible. As applications, we establish the existence of group inverses of certain 2 × 2 block-operator matrices over a Banach space. These generalize the known results, e.g., Zhou, Chen and Zhu (Comm. Algebra48 (2020), 676–690) and Benítez, Liu and Zhu (Linear Multilinear Algebra59 (2011), 279–289). [ABSTRACT FROM AUTHOR]

Copyright of International Journal of Open Problems in Computer Science & Mathematics is the property of International Journal of Open Problems in Computer Science & Mathematics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper presents a new type of semiderivation in ring, called a (f, g)-semiderivation, where f and g are are self-mappings of a ring. We explore various properties of (f, g)-semiderivations and demonstrate that if a semiprime ring R satisfies specific differential identities involving a (f, g)- semiderivation D, then D must be a zero map on R. Additionally, we examine the commutativity of prime rings that admit nonzero (f, g)-semiderivations which satisfy certain differential identities. [ABSTRACT FROM AUTHOR]

In this paper, the concept of centrally extended (α, β)‐higher derivations is studied. It is shown to be additive in a ring without nonzero central ideals. Also, we prove that in semiprime rings with no nonzero central ideals, every centrally extended (α, β)‐higher derivation is an (α, β)‐higher derivation. Some examples are given to show that our theorems' assumptions cannot be relaxed. The invariance problem of the center of the ring is also investigated. [ABSTRACT FROM AUTHOR]

Copyright of Bearing is the property of Bearing Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Bearing is the property of Bearing Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper aims to establish the following: Let Ω be a ring that satisfies some conditions and has an idempotent element f ≠ 0 , 1. We intend to show that if G is any suitable multiplicative generalized CE-derivation of Ω , then G is a centrally extended additive. [ABSTRACT FROM AUTHOR]

Background: Weight recurrence, suboptimal clinical response and functional disorder (such as reflux) after a Sleeve Gastrectomy (SG) are problems that may require conversional surgery. For reflux, conversion to Roux-en-Y Gastric Bypass (RYGB) is considered effective. Regarding treatment for suboptimal clinical response, the technique of choice remains a subject of debate. This study aims to evaluate the safety and effectiveness of conversion from SG to Ring-augmented RYGB (RaRYGB). Methods: All laparoscopic SG to RaRYGB conversions performed between January 2016 and January 2022 were included. Primary outcome was percentage total weight loss (%TWL) after 1-year follow-up. Secondary outcomes consisted of cumulative %TWL, complications (with a focus on ring-related complications), and resolution of medical-associated problems. Results: We included 50 patients of whom 44 were female. Mean pre-conversion BMI was 37.6 kg/m2. All patients have reached the 1-year follow-up point, however 10 were lost to follow-up. After 1-year mean TWL was 17.8% while mean cumulative TWL, calculated from primary SG, was 32%. A total of 10 complications occurred in 8 patients within 30 days, 6 of which were ≤ CD3a and 4 ≥ CD3b. One MiniMizer was removed for complaints of severe dysphagia. Of the 35 medical-associated problems present at screening 5 remained unchanged(14.2%), 15 improved(42.9%) and 15 achieved remission(42.9%). Conclusion: Our series of 50 patients undergoing conversion from SG to RaRYGB is adequate and successful regarding additional weight loss 1 year after conversion, cumulative weight loss, complication rate and achievement of improvement or remission of medical-associated problems. [ABSTRACT FROM AUTHOR]

A map f : R → S {f\colon R\to S} between (associative, unital, but not necessarily commutative) rings is a brachymorphism if f ⁢ ( 1 + x ) = 1 + f ⁢ ( x ) {f(1+x)=1+f(x)} and f ⁢ ( x ⁢ y ) = f ⁢ ( x ) ⁢ f ⁢ ( y ) {f(xy)=f(x)f(y)} whenever x , y ∈ R {x,y\in R} . We tackle the problem whether every brachymorphism is additive (i.e., f ⁢ ( x + y ) = f ⁢ ( x ) + f ⁢ ( y ) {f(x+y)=f(x)+f(y)} ), showing that in many contexts, including the following, the answer is positive: • R is finite (or, more generally, R is left or right Artinian); • R is any ring of 2 × 2 {2\times 2} matrices over a commutative ring; • R is Engelian; • every element of R is a sum of π-regular and central elements (this applies to π-regular rings, Banach algebras, and power series rings); • R is the full matrix ring of order greater than 1 over any ring; • R is the monoid ring K ⁢ [ M ] {K[M]} for a commutative ring K and a π-regular monoid M; • R is the Weyl algebra 햠 1 ⁢ ( K ) {\mathsf{A}_{1}(K)} over a commutative ring K with positive characteristic; • f is the power function x ↦ x n {x\mapsto x^{n}} over any ring; • f is the determinant function over any ring R of n × n {n\times n} matrices, with n ≥ 3 {n\geq 3} , over a commutative ring, such that if n > 3 {n>3} , then R contains n scalar matrices with non zero divisor differences. R is finite (or, more generally, R is left or right Artinian); R is any ring of 2 × 2 {2\times 2} matrices over a commutative ring; R is Engelian;every element of R is a sum of π-regular and central elements (this applies to π-regular rings, Banach algebras, and power series rings); R is the full matrix ring of order greater than 1 over any ring; R is the monoid ring K ⁢ [ M ] {K[M]} for a commutative ring K and a π-regular monoid M; R is the Weyl algebra 햠 1 ⁢ ( K ) {\mathsf{A}_{1}(K)} over a commutative ring K with positive characteristic; f is the power function x ↦ x n {x\mapsto x^{n}} over any ring; f is the determinant function over any ring R of n × n {n\times n} matrices, with n ≥ 3 {n\geq 3} , over a commutative ring, such that if n > 3 {n>3} , then R contains n scalar matrices with non zero divisor differences. [ABSTRACT FROM AUTHOR]

We present a new generalized version of Cline's formula and Jacobson's lemma for g-Drazin inverses in a ring. These generalized results extend many known results, e.g., Chen and Abdolyousefi [Generalized Jacobson's lemma in a Banach algebra, Comm. Algebra49 (2021) 3263–3272], and Yan and Zeng [The generalized inverses of the products of two elements in a ring, Turkish J. Math.44 (2020) 1744–1756]. [ABSTRACT FROM AUTHOR]

Let R be a ring, P a semiprime ideal of R. A map F: R → R is called a multiplicative generalized derivation if there exists a map d: R → R such that F(xy) = F(x)y + xd(y), for all x, y ∈ R. Then, d is P-commuting map on R, if R admits a multiplicative generalized derivation F associated with a nonzero map d such that: (i) [F(x), x] ∈ P, (ii) F(x) ◦ x ∈ P, (iii)F([x, y]) ∈ P,(iv) F(xoy) ∈ P,(v) F([x, y]) ± [G(x), y] ∈ P, (vi)F(xoy) ± (G(x)oy) ∈ P, (vii)[F(x), y] ± [x,G(y)] ∈ P, (viii)F([x, y]) ± (G(x)oy) ∈ P,(ix)F(xoy) ± [G(x), y] ∈ P, (x) F(x)oy ± xoG(y) ∈ P, (xi) F(x)F(y) ± [x, y] ∈ P, (xii) F(x)F(y) ± (x ◦ y) ∈ P, ∀x, y ∈ R [ABSTRACT FROM AUTHOR]

Ubiquitination is an evolutionary, ancient system of post-translational modification of proteins that occurs through a cascade involving ubiquitin activation, transfer, and conjugation. The maturation of this system has followed two main pathways. The first is the conservation of a universal structural fold of ubiquitin and ubiquitin-like proteins, which are present in both Archaea and Bacteria, as well as in multicellular Eukaryotes. The second is the rise of the complexity of the superfamily of ligases, which conjugate ubiquitin-like proteins to substrates, in terms of an increase in the number of enzyme variants, greater variation in structural organization, and the diversification of their catalytic domains. Here, we examine the diversity of the ubiquitination system among different organisms, assessing the variety and conservation of the key domains of the ubiquitination enzymes and ubiquitin itself. Our data show that E2 ubiquitin-conjugating enzymes of metazoan phyla are highly conservative, whereas the homology of E3 ubiquitin ligases with human orthologues gradually decreases depending on "molecular clock" timing and evolutionary distance. Surprisingly, Chordata and Echinodermata, which diverged over 0.5 billion years ago during the Cambrian explosion, share almost the same homology with humans in the amino acid sequences of E3 ligases but not in their adaptor proteins. These observations may suggest that, firstly, the E2 superfamily already existed in its current form in the last common metazoan ancestor and was generally not affected by purifying selection in metazoans. Secondly, it may indicate convergent evolution of the ubiquitination system and highlight E3 adaptor proteins as the "upper deck" of the ubiquitination system, which plays a crucial role in chordate evolution. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of the intrinsic product of neutrosophic sets, and some related properties are investigated. Characterizations of neutrosophic subrings, neutrosophic ideals, neutrosophic quasi-ideals, and neutrosophic bi-ideals are given. [ABSTRACT FROM AUTHOR]

In this paper, left and right (v, w)-weighted (b, c)-inverse in rings are introduced. Let R be a ring and a, b, c, v, w ∈ R. The element x ∈ R is called a left (v, w)-weighted (b, c)-inverse of a if Rx ∈ Rc and xvawb = b and dually y ∈ R is called a right (v, w)-weighted (b, c)-inverse of a if yR ⊆ bR and cvawy = c. Existence criteria for left and right (v, w)-weighted (b, c)-inverse of a are given. We also present explicit expressions for left and right weighted (b, c)-inverse by using inner inverses. As applications, several equivalent conditions for an element in a ring to be (v, w)-weighted (b, c)-invertible are obtained. Moreover, commuting properties of the (v, w)-weighted (b, c)-inverse are investigated. [ABSTRACT FROM AUTHOR]

Let G = (V, E) be a simple graph and (R, +, ·) be a ring with zero element 0R. The Wiener index of G, denoted by W(G), is defined as the sum of distances of every vertex u and v, or half of the sum of all entries of its distance matrix. The prime graph of R, denoted by P G(R), is defined as a graph with V (P G(R)) = R such that uv ∈ E(P G(R)) if and only if uRv = {0R} or vRu = {0R}. In this article, we determine the Wiener index of P G(Zn) in some cases n by constructing its distance matrix. We partition the set Zn into three types of sets, namely zero sets, nontrivial zero divisor sets, and unit sets. There are two objectives to be achieved. Firstly, we revise the Wiener index formula of P G(Zn) for n = p² and n = p³ for prime number p and we compare this results with the results carried out by previous researchers. Secondly, we determine the Wiener index formula of P G(Zn) for n = pq, n = p² q, n = p² q², and n = pqr for distinct prime numbers p, q, and r. [ABSTRACT FROM AUTHOR]

This paper presents an analysis of the results of the ring rolling process of EN AW-7075 aluminium alloy using numerical modelling. The study of the rheological properties of the AW-7075 aluminium alloy was carried out using the Gleeble 3800 metallurgical process simulator. The modelling of the ring rolling process in the experimental mill was carried out using the Simufact Forming programme based on the finite element method. Based on the analysis of the test results, the speed of the mandrel, the speed of the main roll, the temperature of the metal at the beginning and at the end of the rolling process were determined. The results of research were verified in an experimental mill. [ABSTRACT FROM AUTHOR]

In the context of training and developing the skills of teachers, students and children to solve exercises and problems in Mathematics, in this paper we propose to continue the steps started in the first three papers with the same generic title and marked symbolically with (I), (II), respectively with (III) namely, the presentation of some ways of achieving a systemic vision on a certain notional mathematical content, a vision that motivates and mobilizes the activity of those who teach in the classroom, thus facilitating both the teaching and the assimilation of the concepts, concepts, and scientific theories addressed of the educational disciplines that present phenomena and processes from nature. Thus, we will continue in the same systemic approach, solving some Diophantine equations of higher degree, more precisely some generalizations of the Pythagorean equation and some quadratic Diophantine equations, in the set of natural numbers, then of the whole numbers, in order to "submerge" a such an equation in a ring of matrices and try to find as many matrix solutions as possible. The methods used, in this work, in solving the Diophantine equations, are diversified and different, for the most part, from those used in previous works of this type. It will result, then, that the methods of solving matrix equations related to these equations will follow the same direction. To facilitate the reader's understanding of the solutions of these matrix equations, in some cases we have also presented examples. [ABSTRACT FROM AUTHOR]

In chemistry, graph theory has been widely utilized to address molecular problems, with numerous applications in graph theory and ring theory within this field. One of these applications involves topological indices that represent chemical structures with numerical values. Various types of topological indices exist, including the Wiener index, the first Zagreb index, and the hyperWiener index. In the context of this research, the values of the Wiener index, the first Zagreb index, and the hyper-Wiener index for zero-divisor graphs on the ring of integers modulo a prime power order will be explored through a literature review and conjecture. [ABSTRACT FROM AUTHOR]

This research paper covers a comprehensive investigation into the design, analysis, and performance evaluation of frequency reconfigurable antennas. The relentless advancement of wireless communication technology has necessitated the development of antennas that can adapt seamlessly to a wide range of operating frequencies. The proposed antenna design incorporates a circular ring configuration with a PIN diode for dynamic frequency tuning. The reconfigurable element allows for versatile operation across multiple frequency bands, avoiding the requirement for separate antennas and simplifying system integration. The performance evaluation encompasses key parameters such as radiation pattern, gain, bandwidth, and efficiency, assuring optimal performance across the specified frequency range. The measured and simulated results validate the accuracy and effectiveness of the recommended structure. The research findings contribute to the state-of-the-art advancements in frequency reconfigurable antenna engineering, enabling efficient wireless communication systems for several applications, such as cellular networks, WLANs, satellite communication systems, and cognitive radio networks. [ABSTRACT FROM AUTHOR]

It is not known whether or not every non-zero one-sided nil ideal of a noncommutative ring is contained in the upper nilradical of the ring. Here we give necessary and sufficient conditions under which a non-zero one-sided nil ideal of a noncommutative ring is not contained in the upper nilradical of the ring. [ABSTRACT FROM AUTHOR]

Let $\wp$ be a ring. It is shown that if an additive mapping $\vartheta$ is a zero-power valued on $\wp$, then $\alpha:\wp\rightarrow\wp$ such that $\alpha=\vartheta+1$ is a bijective mapping of $\wp.$ The main aim of this study is to prove that $\vartheta$ is a homoderivation of $\wp$ if and only if $\vartheta:\wp\rightarrow\wp$ such that $\vartheta=\alpha-1$ is a semi-derivation associated with $\alpha$, where $\alpha:\wp\rightarrow\wp$ is a homomorphism of $\wp.$ Moreover, if $\vartheta$ is a zero-power valued homoderivation on $\wp,$ then $\vartheta$ is a semi-derivation associated with $\alpha$, where $\alpha :\wp\rightarrow\wp$ is an automorphism of $\wp$ such that $\alpha=\vartheta+1$.

The necessity of stabilization of ring blanks of low rigidity is substantiated. For stabilization a 6-position loading scheme with uniformly distributed radial forces is proposed, with the possibility to transform into 3- and 2-position loading schemes. The stress state of the ring under loading by uniformly distributed radial forces is analyzed, and calculation dependences for determining the total stress at 6-, 3- and 2-position loading schemes are proposed. Calculation dependences are offered for determination of force parameters of the device with lever-joint mechanism for creation of stresses in the ring at the level of conditional yield strength. According to the proposed method of calculation of force parameters, an example of calculation is given for a ring made of 40ХМФА (40KhMFA) steel with an outside diameter of 392 mm. The developed recommendations can be used at creation of devices for stabilization and removal of residual stresses in ring blanks, which are necessary for manufacture of critical products in such areas as auto- and aircraft construction, precision engineering, military industry.

The Smc5/6 complex is a highly conserved molecular machine involved in the maintenance of genome integrity. While its functions largely depend on restraining the fork remodeling activity of Mph1 in yeast, the presence of an analogous Smc5/6-FANCM regulation in humans remains unknown. We generated human cell lines harboring mutations in the NSE1 subunit of the Smc5/6 complex. Point mutations or truncations in the RING domain of NSE1 result in drastically reduced Smc5/6 protein levels, with differential contribution of the two zinc-coordinating centers in the RING. In addition, nse1-RING mutant cells display cell growth defects, reduced replication fork rates, and increased genomic instability. Notably, our findings uncover a synthetic sick interaction between Smc5/6 and FANCM and show that Smc5/6 controls fork progression and chromosome disjunction in a FANCM-independent manner. Overall, our study demonstrates that the NSE1 RING domain plays vital roles in Smc5/6 complex stability and fork progression through pathways that are not evolutionary conserved. [ABSTRACT FROM AUTHOR]

We extend the concept of a G-Drazin inverse from the set M n of all n × n complex matrices to the set R D of all Drazin invertible elements in a ring R with identity. We also generalize a partial order induced by G-Drazin inverses from M n to the set of all regular elements in R D , study its properties, compare it to known partial orders, and generalize some known results. [ABSTRACT FROM AUTHOR]

Copyright of Bearing is the property of Bearing Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, we establish six necessary and sufficient conditions for a homeomorphism of R n onto itself to be strongly quasisymmetric. These conditions are quantitative in terms of conformal moduli of disjoint continua as well as the geometric modulus, which was recently introduced by Tukia and Väisälä. Note that all of them are equivalent to bilipschitz continuity with parameters depending also on two fixed points. As an application, we obtain several quantitative characterizations for a homeomorphism of the Riemann sphere R ¯ n onto itself to be strongly quasimöbius. [ABSTRACT FROM AUTHOR]

The subject of research: The rule of Engagement ring in Islam. Name of the researcher: Dr. Muhammad bin Saeed bin Kadam. The aim of the research: Islamic ruling Clarificadion for each case of wearing engagement ring or the marriage. Research Method: The inductive and analytical approaches. The main results: 1. Wearing an engagement ring if its owner believes that it brings love and affection, or that it removes hostility between spouses, then wearing it is forbidden and the believer must avoid this act. 2. If the suitor or fiancée wears a ring to indicate his or her engagement, the most likely opinion-and God knows best-is that this is permissible, provided that he does not believe in this custom any belief that contradicts Islamic law. Main recommendations: 1. Must warn all muslims about wrong beliefs about engagement ring, for example: I think it could be the reason for love and happiness between the couple. 2. Must differentiate between who wears it just for announcement and who wears it for corrupt beliefs that violate islamic rules. [ABSTRACT FROM AUTHOR]