Invariants and isomorphism theorems for zero-divisor graphs of commutative rings of quotients
نویسندگان
چکیده
منابع مشابه
On quasi-zero divisor graphs of non-commutative rings
Let $R$ be an associative ring with identity. A ring $R$ is called reversible if $ab=0$, then $ba=0$ for $a,bin R$. The quasi-zero-divisor graph of $R$, denoted by $Gamma^*(R)$ is an undirected graph with all nonzero zero-divisors of $R$ as vertex set and two distinct vertices $x$ and $y$ are adjacent if and only if there exists $0neq rin R setminus (mathrm{ann}(x) cup mathrm{ann}(y))$ such tha...
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In this paper we will investigate the interactions between the zero divisor graph, the annihilator class graph, and the associate class graph of commutative rings. Acknowledgements: We would like to thank the Center for Applied Mathematics at the University of St. Thomas for funding our research. We would also like to thank Dr. Michael Axtell for his help and guidance, as well as Darrin Weber f...
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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 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...
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We recall several results of zero divisor graphs of commutative rings. We then examine the preservation of the diameter of the zero divisor graph of polynomial and power series rings.
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ژورنال
عنوان ژورنال: Journal of Commutative Algebra
سال: 2014
ISSN: 1939-2346
DOI: 10.1216/jca-2014-6-3-407