منابع مشابه
Infinite Rings with Planar Zero-divisor Graphs
For any commutative ring R that is not a domain, there is a zerodivisor graph, denoted Γ(R), in which the vertices are the nonzero zero-divisors of R and two distinct vertices x and y are joined by an edge exactly when xy = 0. In [Sm2], Smith characterized the graph structure of Γ(R) provided it is infinite and planar. In this paper, we give a ring-theoretic characterization of R such that Γ(R)...
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In this paper we give a characterization for all commutative rings with $1$ whose zero-divisor graphs are $C_4$-free.
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For an arbitrary ring $R$, the zero-divisor graph of $R$, denoted by $Gamma (R)$, is an undirected simple graph that its vertices are all nonzero zero-divisors of $R$ in which any two vertices $x$ and $y$ are adjacent if and only if either $xy=0$ or $yx=0$. It is well-known that for any commutative ring $R$, $Gamma (R) cong Gamma (T(R))$ where $T(R)$ is the (total) quotient ring of $R$. In this...
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In this paper, we introduce a family of graphs which is a generalization of zero-divisor graphs and compute an upper-bound for the diameter of such graphs. We also investigate their cycles and cores
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in this paper we give a characterization for all commutative rings with $1$ whose zero-divisor graphs are $c_4$-free.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2007
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2007.01.049