Results 11 to 20 of about 172 (46)
Indecomposable modules and Gelfand rings [PDF]
, 2007 It is proved that a commutative ring is clean if and only if it is Gelfand with a totally disconnected maximal spectrum. Commutative rings for which each indecomposable module has a local endomorphism ring are studied.
Bkouche R. +5 more
core +3 more sources
, 2010 The Image Conjecture was formulated by the third author, who showed that it implied his Vanishing Conjecture, which is equivalent to the famous Jacobian Conjecture.
Essen, Arno van den +2 more
core +4 more sources
Commutative rings with homomorphic power functions
International Journal of Mathematics and Mathematical Sciences, Volume 15, Issue 1, Page 91-102, 1992., 1991 A (commutative) ring R (with identity) is called m‐linear (for an integer m ≥ 2) if (a+b)m = am + bm for all a and b in R. The m‐linear reduced rings are characterized, with special attention to the finite case. A structure theorem reduces the study of m‐linearity to the case of prime characteristic, for which the following result establishes an ...
David E. Dobbs +2 more
wiley +1 more source
, 2015 Let C.R/ denote the center of a ring R and g.x/ be a polynomial of ring C.R/Œx. An element r 2 R is called “g.x/-clean” if r D sCu where g.s/D 0 and u is a unit of R and R is g.x/-clean if every element is g.x/-clean.
N. Ashrafi, Z. Ahmadi
semanticscholar +1 more source
Computing metric dimension of compressed zero divisor graphs associated to rings
Acta Universitatis Sapientiae: Mathematica, 2018 For a commutative ring R with 1 ≠ 0, a compressed zero-divisor graph of a ring R is the undirected graph ΓE(R) with vertex set Z(RE) \ {[0]} = RE \ {[0], [1]} defined by RE = {[x] : x ∈ R}, where [x] = {y ∈ R : ann(x) = ann(y)} and the two distinct ...
Pirzada S., Bhat M. Imran
doaj +1 more source
A Short Note on the Primary Submodules of Multiplication Modules
, 2007 Let M be an R-module. An R-module M is called multiplication if for any submodule N of M we have N = IM, where I is an ideal of R. In this paper we characterize primary submodules of multiplication modules.
S. E. Atani +2 more
semanticscholar +1 more source
Zero-Divisor Graphs of Idealizations with Respect to Prime Modules
, 2007 Let R be a commutative ring with identity and let M be a prime Rmodule. Let R(+)M be the idealization of the ring R by the R-module M. We study the diameter and girth of the zero-divisor graph of the ring R(+)M. Mathematics Subject Classification: 13A99,
S. E. Atani, Z. E. Sarvandi
semanticscholar +1 more source
Finitely generated abelian groups of units [PDF]
, 2019 In 1960 Fuchs posed the problem of characterizing the groups which are the groups of units of commutative rings. In the following years, some partial answers have been given to this question in particular cases.
Del Corso, Ilaria
core +2 more sources
Rings Graded By a Generalized Group
Topological Algebra and its Applications, 2014 The aim of this paper is to consider the ringswhich can be graded by completely simple semigroups.We show that each G-graded ring has an orthonormal basis, where G is a completely simple semigroup. Weprove that if I is a complete homogeneous ideal of a G-
Fatehi Farzad, Molaei Mohammad Reza
doaj +1 more source
Modules satisfying the prime and maximal radical conditions
, 2014 In this paper, we introduce and study Pradical and M-radical modules over commutative rings. We say that an R-module M is P-radical whenever M satisfies the equality ( p √ PM : M) = √ P for every prime ideal P ⊇ Ann(PM), where p √ PM is the intersection ...
M. Behboodi, M. Sabzevari
semanticscholar +1 more source