The Zero-Divisor Graph of a Commutative Ring
نویسندگان
چکیده
منابع مشابه
On the Zero-divisor Cayley Graph of a Finite Commutative Ring
Let R be a fnite commutative ring and N(R) be the set of non unit elements of R. The non unit graph of R, denoted by Gamma(R), is the graph obtained by setting all the elements of N(R) to be the vertices and defning distinct vertices x and y to be adjacent if and only if x - yin N(R). In this paper, the basic properties of Gamma(R) are investigated and some characterization results regarding co...
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Ž . Ž . Let R be a commutative ring with 1 and let Z R be its set of Ž . Ž . zero-divisors. We associate a simple graph G R to R with vertices Ž . Ž . 4 Z R * s Z R y 0 , the set of nonzero zero-divisors of R, and for disŽ . tinct x, y g Z R *, the vertices x and y are adjacent if and only if xy s 0. Ž . Thus G R is the empty graph if and only if R is an integral domain. The main object of this...
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متن کاملTHE ZERO-DIVISOR GRAPH OF A MODULE
Let R be a commutative ring with identity and M an R-module. In this paper, we associate a graph to M, sayΓ(RM), such that when M=R, Γ(RM) coincide with the zero-divisor graph of R. Many well-known results by D.F. Anderson and P.S. Livingston have been generalized for Γ(RM). We Will show that Γ(RM) is connected withdiam Γ(RM)≤ 3 and if Γ(RM) contains a cycle, then Γ(RM)≤4. We will also show tha...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1999
ISSN: 0021-8693
DOI: 10.1006/jabr.1998.7840