When Intersection Ideals of Graphs of Rings are a Divisor graph
نویسندگان
چکیده
منابع مشابه
On cycles in intersection graphs of rings
Let $R$ be a commutative ring with non-zero identity. We describe all $C_3$- and $C_4$-free intersection graph of non-trivial ideals of $R$ as well as $C_n$-free intersection graph when $R$ is a reduced ring. Also, we shall describe all complete, regular and $n$-claw-free intersection graphs. Finally, we shall prove that almost all Artin rings $R$ have Hamiltonian intersection graphs. ...
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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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متن کاملon cycles in intersection graphs of rings
let $r$ be a commutative ring with non-zero identity. we describe all $c_3$- and $c_4$-free intersection graph of non-trivial ideals of $r$ as well as $c_n$-free intersection graph when $r$ is a reduced ring. also, we shall describe all complete, regular and $n$-claw-free intersection graphs. finally, we shall prove that almost all artin rings $r$ have hamiltonian intersection graphs. ...
متن کاملZero-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.
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ژورنال
عنوان ژورنال: WSEAS TRANSACTIONS ON MATHEMATICS
سال: 2020
ISSN: 1109-2769
DOI: 10.37394/23206.2020.19.44