منابع مشابه
Zero-divisor and Ideal-divisor Graphs of Commutative Rings
For a commutative ring R, we can form the zero-divisor graph Γ(R) or the ideal-divisor graph ΓI(R) with respect to an ideal I of R. We consider the diameters of direct products of zero-divisor and ideal-divisor graphs.
متن کاملOn L-ideal-based L-zero-divisor Graphs
In a manner analogous to a commutative ring, the L-ideal-based L-zero-divisor graph of a commutative ring R can be defined as the undirected graph Γ(μ) for some L-ideal μ of R. The basic properties and possible structures of the graph Γ(μ) are studied.
متن کاملZero-divisor Graphs of Amalgamated Duplication of a Ring along an Ideal
Let R be a commutative ring with identity and let I be an ideal of R. Let R 1 I be the subring of R×R consisting of the elements (r,r + i) for r ∈ R and i ∈ I. We study the diameter and girth of the zero-divisor graph of the ring R 1 I.
متن کاملOn zero-divisor graphs of quotient rings and complemented zero-divisor graphs
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...
متن کاملA generalization of zero-divisor graphs
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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ژورنال
عنوان ژورنال: Involve, a Journal of Mathematics
سال: 2015
ISSN: 1944-4184,1944-4176
DOI: 10.2140/involve.2015.8.87