Results 71 to 80 of about 335,227 (157)
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
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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
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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.
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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
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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
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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
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Upper dimension and bases of zero-divisor graphs of commutative rings
AKCE International Journal of Graphs and Combinatorics, 2020 For a commutative ring with non-zero zero divisor set , the zero divisor graph of is with vertex set , where two distinct vertices and are adjacent if and only if .
S. Pirzada, M. Aijaz, S.P. Redmond
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On Prime Rings with Derivations
AxiomsThis paper identifies all derivations associated with two well-known non-commutative prime rings and provides some remarks on one of these derivations, called the prime derivation.
Khalid H. Al-Shaalan
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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.
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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.
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