Zero-Divisor Graph with Respect to an Ideal
نویسندگان
چکیده
منابع مشابه
Zero-Divisor Graph with Respect to an Ideal*
Let R be a commutative ring with nonzero identity and let I be an ideal of R. The zero-divisor graph of R with respect to I, denoted by ΓI(R), is the graph whose vertices are the set {x ∈ R \ I| xy ∈ I for some y ∈ R \ I} with distinct vertices x and y adjacent if and only if xy ∈ I. In the case I = 0, Γ0(R), denoted by Γ(R), is the zero-divisor graph which has well known results in the literat...
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Let $M$ be an $R$-module and $0 neq fin M^*={rm Hom}(M,R)$. We associate an undirected graph $gf$ to $M$ in which non-zero elements $x$ and $y$ of $M$ are adjacent provided that $xf(y)=0$ or $yf(x)=0$. Weobserve that over a commutative ring $R$, $gf$ is connected anddiam$(gf)leq 3$. Moreover, if $Gamma (M)$ contains a cycle,then $mbox{gr}(gf)leq 4$. Furthermore if $|gf|geq 1$, then$gf$ is finit...
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Let N be a near-ring. In this paper, we associate a graph corresponding to the 3-prime radical I of N , denoted by ΓI(N). Further we obtain certain topological properties of Spec(N), the spectrum of 3-prime ideals of N and graph theoretic properties of ΓI(N). Using these properties, we discuss dominating sets and connected dominating sets of ΓI(N).
متن کاملa module theoretic approach to zero-divisor graph with respect to (first) dual
let $m$ be an $r$-module and $0 neq fin m^*={rm hom}(m,r)$. we associate an undirected graph $gf$ to $m$ in which non-zero elements $x$ and $y$ of $m$ are adjacent provided that $xf(y)=0$ or $yf(x)=0$. weobserve that over a commutative ring $r$, $gf$ is connected anddiam$(gf)leq 3$. moreover, if $gamma (m)$ contains a cycle,then $mbox{gr}(gf)leq 4$. furthermore if $|gf|geq 1$, then$gf$ is finit...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2006
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927870500441858