Search

A significant development in the field of gyrogroups was the introduction of the space of all relativistically admissible velocities, which brought gyrogroups into the mainstream. A group has various generalizations, one of which is the notion of gyrogroups. Moreover, for any pair (a; b) in this structure, there exists an automorphism gyr[a; b] that fulfills left associativity and left loop property. The motivation behind this study is to generalize gyrogroups and semigroups, which has led to the introduction of gyrosemigroups. Accordingly, in this paper, some classes of gyrosemigroups are presented. Also, all gyrosemigroups of order 2 are characterized. Furthermore, the gyrosemigroups with an identity or a zero are studied. [ABSTRACT FROM AUTHOR]

The initiation and majority on rough sets for algebraic hyperstructures such as hypermodules over a hyperring have been concentrated on a congruence relation. The congruence relation, however, seems to restrict the application of the generalized rough set model for algebraic sets. In this paper, in order to solve this problem, we consider the concept of set-valued homomorphism for hypermodules and we give some examples of set-valued homomorphism. In this respect, we show that every homomorphism of the hypermodules is a set-valued homomorphism. The notions of generalized lower and upper approximation operators, constructed by means of a set-valued mapping, which is a generalization of the notion of lower and upper approximations of a hypermodule, are provided. We also propose the notion of generalized lower and upper approximations with respect to a subhypermodule of a hypermodule discuss some significant properties of them.

In this paper, we extend the notion of Hv-semigroups to neutro-Hv-semigroups and anti-Hv-semigroups and investigate many of their properties. We show that these new concepts are different from the classical concept of Hv-semigroups by presenting several examples. In general, the neutro-algebras and anti-algebras are generalizations and alternatives of classical algebras. The goal and benefits of our proposed extension of this study is to explore not only the hyperoperations and axioms that are totally true as in previous algebraic hyperstructures, but also the cases when they have degrees of truth, indeterminacy and falsehood. Therefore, we enlarge the field of research. [ABSTRACT FROM AUTHOR]

Copyright of Journal of the Indonesian Mathematical Society is the property of Indonesian Mathematical Society 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.)

We say that (R, f, g) is an additive (m, n)-semihyperring if R is a non-empty set, f is an m-ary associative hyperoperation, g is an n-ary associative operation and g is distributive with respect to f. In this paper, we describe a number of characterizations of additive (m, n)-semihyperrings which generalize well-known results. Also, we consider distinguished elements, hyperideals, Rees factors and regular relations. Later, we give a natural method to derive the quotient (m, n)-semihyperring. [ABSTRACT FROM AUTHOR]