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For several classes of special p-groups G, of exponent p, p > 2, we show that the near-ring, C 0 ( G ) , of congruence preserving functions on G is a ring if and only if G is a 1-affine complete group.

Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_0 (G)$$\end{document}C0(G) denote the near-ring of congruence preserving functions of the group G. We investigate the question “When is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_0 (G)$$\end{document}C0(G) a ring?”. We obtain information externally via the lattice structure of the normal subgroups of G and internally via structural properties of the group G.

For several classes of groups G, we characterize when the near-ring M0(G) of 0-preserving selfmaps on G contains a unique maximal ring. Definitive results are obtained for finite Abelian, finite ni...

Contains fulltext : 172136.pdf (Publisher’s version ) (Open Access) OBJECTIVE(S): The ultrasonic advanced energy study device (AH device) is the first surgical device indicated to seal vessels up to and including 7mm using ultrasonic technology alone. This study assesses clinical experience during total laparoscopic hysterectomy (TLH) using advanced hemostasis mode (AHM). STUDY DESIGN: This was a prospective, non-randomized, single arm, multicenter, observational study which did not modify or influence current surgeon technique for elective TLH for benign disease. Each surgeon assessed hemostasis, defined as the hemostatic transection of the uterine vasculature (left/right) with at least one use of the AH device in AHM without the use of additional hemostatic measures other than the AH device. Patients were followed for 4-6 weeks after surgery. Vessel sealing performance was quantitatively assessed for transection and sealing of the uterine artery (UA), the uterine pedicle (UP; defined as cases where the UA could not be 'isolated') and the ovarian pedicle (OP) (when indicated). Adverse events (AEs) related to the AH device or procedures were collected. RESULTS: Forty patients underwent the procedure. Mean age was 49 years and mean body mass index was 28kg/m(2). Mean surgical duration was 88min. None required conversion to open procedure. Using only the AH device, hemostasis was achieved and maintained in 119 (94.4%) transections (both left and right sides of the UA/UP and OP). Additional hemostasis was achieved in 5 patients using conventional bipolar (4) or monopolar (1) energy. No patient required a blood transfusion postoperatively. Only one adverse event of pain was considered to be related to the use of the ultrasonic AH device during this study. CONCLUSION: These results support that the AH device with its AHM has clinical utility in sealing named vessels in TLH. The new algorithm to deliver energy in the AHM has the potential to reduce the need for additional hemostatic devices or products as well as the potential to reduce the need for multiple instrument changes during surgery.

In this paper we continue the investigation of properties of mutations of commutative monoids. In particular, we consider mutation semigroups, $$M$$ , of free $$2$$ -generated commutative monoids and show that the semirings of endomorphisms of $$M$$ are maximal semirings in the collection of selfmaps of $$M$$ .

We define and use a Galois correspondence to determine, for certain medial semigroups, S, some maximal semirings in the collection M(S) of self maps on S.

Click on the link to view the abstract. Keywords: Mutations of commutative monoids, endomorphism semirings Quaestiones Mathematicae 36(2013), 477–485

For a finite group G and a cover C of G by cyclic subgroups, we investigate the structure of the associated ring R ( C ) . General results are obtained which are then applied to obtain specific results on several classes of groups.

For a finite group G with a cover by abelian subgroups, consider the ring of functions that act as endomorphisms on each subgroup in the cover. Properties of this ring are explored. In particular, conditions for and consequences of simplicity are investigated.

For a group G, let M(G) denote the near-ring of functions on G. We characterize all maximal subnear-rings of M(G) and show that for many classes of groups, E(G), the near-ring generated by the semigroup, End(G) of G, is never maximal as a subnear-ring of M0 (G).

For a finite group G, let E(G) denote the near-ring of functions generated by the semigroup, End(G), of endomorphisms of G. We characterize when E(G) is maximal as a subnear-ring of M o(G). A group G is an E-group if E(G) is a ring. We give a new characterization of finite E-groups and investigate the problem of determining, for finite E-groups, when E(G) is maximal as a ring in Mo(G).

We documented nest habitat selection, nests success, and factors affecting nest success of Black Terns (Chlidonias niger) at Agassiz National Wildlife Refuge in northwestern Minnesota. During 1992-1994, 289 Black Tern nest sites and 400 random sites were sampled on five search areas totaling 1,325 ha. Four habitat characteristics were measured at each nest and random site: (1) mean water depth, (2) distance to open water, (3) dominant vegetation within a 2-m radius, and (4) amount of open water within a 2-m radius. Habitat variables were highly correlated with each other, making it difficult to estimate independent effects of each habitat variable on nest-site selection. However, conditional logistic regression models indicated that locations closer to open water and in deeper water were more likely to be associated with nest sites. Locations in bulrush (Scirpus acutus) and sedge/grass were preferred, although 68% of nests were in cattail (Typha spp.) reflecting the greater availability of that h...

An R-module V is a ray if for every R-module W, the R-homogeneous functions from V to W are additive. We use properties of the lattice of submodules of \( V, {\cal L}(V) \), to determine conditions for V to be a ray. We also use the lattice structure of \( {\cal L}(V) \) to further study those rings such that every R-module V is a ray. As a result, we can characterize all semisimple modules which are rays.

A derivation d on a ring R is simple if the only ideals of R invariant under d are the trivial ideals {0} and R. In this work we show a new proof that, for affine k-algebras, R = k[x 1,…, x n ]/I where k is a field and I is a homogeneous ideal, simple derivations exist if and only if I has a rather restrictive form. Some examples of simple derivations on these algebras are then presented.

Let e be the collection of those rings S such that, for every S-module V and every homogeneous function ƒ. V → V, ƒ(sv) = sƒ(v), s ∈ S, v ∈ V, ƒ is linear on V. In this paper we characterize those Stanley-Reisner rings, R, such that D(R) is in e.

If R is a simple Noetherian ring and V an R-module, then every homogeneous function on V is an endomorphism, i.e., the forcing linearity number, fln(V), of V is zero, unless R is a domain. Here we consider the problem of finding forcing linearity numbers for modules over simple Noetherian domains. As an application we find the forcing linearity numbers for all finitely generated modules over the first Weyl algebra.

The forcing linearity numbers for projective modules over commutative Noetherian rings are completely determined.

In this paper the forcing linearity numbers for injective modules over principal ideal domains are determined. As a consequence one obtains the forcing linearity numbers for divisible abelian groups.

Let R be a finite commutative ring. In this paper, the authors derive an upper bound for the total number of functions from R to itself which can be represented by polynomials over R. A necessary condition on R for the upper bound to be obtained is also provided. These results generalize known results for Galois rings.

For a module over a ring R we introduce the concept of a forcing linearity number which is a type of measure of how much local linearity is needed to imply global linearity. We determine this number for vector spaces, for modules over integral domains, not fields, and for modules over local rings, not integral domains.

Let M be a maximal submodule of an R-module V. Let f:V→V be a map with f(rv)=rf(v),r∈R,v∈V. In this paper we consider the problem of determining when f∈HomR(M,V) implies f∈EndRV.

An idealI of the ringK[x1, ...,x n ] of polynomials over a fieldK inn indeterminates is a full ideal ifI is closed under substitution,f eI,g1...gn eK[x1, ...,x n ] implyf(g1, ...,g n ) eI. In this paper we continue the investigation of full ideals ofK[x1, ...,x n ]. In particular we determine several classes of full ideals ofK[x, y] (K a finite field) and investigate properties of these classes.