Results 1 to 10 of about 327,963 (245)
Quasi-Regular Graphs Associated with Commutative Rings
Journal of Mathematics, 2022 One of the most important branches of mathematics is algebraic graph theory, which solves graph problems with algebraic methods. In graph theory, several algebraic properties of a ring can be represented.
Nasr Zeyada +2 more
doaj +1 more source
Acyclic Complexes and Graded Algebras
Mathematics, 2023 We already know that the noncommutative N-graded Noetherian algebras resemble commutative local Noetherian rings in many respects. We also know that commutative rings have the important property that every minimal acyclic complex of finitely generated ...
Chaoyuan Zhou
doaj +1 more source
Journal of the Korean Mathematical Society, 2016 The authors define a ring \(R\) (associative with identity) to be \textit{quasi-commutative} if \(ab\) is in the center of \(R\) for all \(a\in C_{f(x)}\) and \(b\in C_{g(x)}\) whenever \(f(x)\) and \(g(x)\) are in the center of the polynomial ring \(R[x]\). Here \(C_{h(x)}\) denotes the set of all coefficients of the polynomial \(h(x)\).
Jung, Da Woon +7 more
openaire +2 more sources
NON-NILPOTENT GRAPH OF COMMUTATIVE RINGS [PDF]
Journal of Algebraic SystemsLet R be a commutative ring with unity. Let Nil(R) be the set of all nilpotent elements of R and Nil(R) = R \ Nil(R) be the set of all non-nilpotent elements of R. The non-nilpotent graph of R is a simple undirected graph GNN(R) with Nil(R) as vertex set
Hussain Mohammed Imdadul Hoque +3 more
doaj +1 more source
UNIFORMLY N-IDEALS OF COMMUTATIVE RINGS [PDF]
Journal of Algebraic SystemsIn this paper, we introduce the concept of uniformly $n$-ideal ofcommutative rings which is a special type of $n$-ideal. We call aproper ideal $I$ of $R$ a uniformly $n$-ideal if there exists apositive integer $k$ for $a,b\in R$ whenever $ab\in I$ and$a ...
Mohammad Baziar +2 more
doaj +1 more source
n-absorbing I-primary ideals in commutative rings
Tikrit Journal of Pure Science, 2023 We define a new generalization of n-absorbing ideals in commutative rings called n-absorbing I-primary ideals. We investigate some characterizations and properties of such new generalization. If P is an n-absorbing I-primary ideal of R and √IP=I√P, then
Sarbast A. Anjuman, Ismael Akray
doaj +1 more source
On commutative endomorphism rings [PDF]
Pacific Journal of Mathematics, 1970 This note deals with a finitely generated faithful module E over a commutative semi-prime noetherian ring R, with commutative endomorphism ring HomJ2(Er, E) = Ω(E). It is shown that E is identifiable to an ideal of R whenever Ω(E) lacks nilpotent elements; a class of examples with Ω(E) commutative but not semi-prime is discussed.
openaire +2 more sources
Z-Polynomials and Ring Commutativity [PDF]
Mathematical Proceedings of the Royal Irish Academy, 2012 We characterise polynomials f with integer coefficients such that a ring with unity R is necessarily commutative if f(x) is central for all x Ɛ R. We also solve the corresponding problem without the assumption that the ring has a unity.
Buckley, Stephen M., McHale, D.
openaire +2 more sources
Characterization of rings with planar, toroidal or projective planar prime ideal sum graphs
AKCE International Journal of Graphs and CombinatoricsLet R be a commutative ring with unity. The prime ideal sum graph [Formula: see text] of the ring R is the simple undirected graph whose vertex set is the set of all nonzero proper ideals of R and two distinct vertices I and J are adjacent if and only if
Praveen Mathil +3 more
doaj +1 more source
On Commutativity Theorems for Rings [PDF]
Southeast Asian Bulletin of Mathematics, 2002 The author presents three commutativity theorems for rings. There are no rings satisfying the hypotheses of the first, and the second is trivial. The third, which asserts that a ring with 1 is commutative if it satisfies the identity \((x+y)^2=x^2+y^2\) and another extraneous hypothesis, is not new. In fact, \textit{C.-T.
openaire +2 more sources