Automorphisms of Zero Divisor Graphs of Cube Radical Zero Completely Primary Finite Rings
نویسندگان
چکیده
منابع مشابه
On 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 کاملUnit groups of cube radical zero commutative completely primary finite rings
A completely primary finite ring is a ring R with identity 1 = 0 whose subset of all its zero divisors forms the unique maximal ideal J . Let R be a commutative completely primary finite ring with the unique maximal ideal J such that J3 = (0) and J2 = (0). Then R/J ∼= GF(pr) and the characteristic of R is pk, where 1≤ k ≤ 3, for some prime p and positive integer r. Let Ro =GR(pkr , pk) be a Gal...
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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...
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 کاملZero-Divisor Graphs and Lattices of Finite Commutative Rings
In this paper we consider, for a finite commutative ring R, the wellstudied zero-divisor graph Γ(R) and the compressed zero-divisor graph Γc(R) of R and a newly-defined graphical structure — the zero-divisor lattice Λ(R) of R. We give results which provide information when Γ(R) ∼= Γ(S), Γc(R) ∼= Γc(S), and Λ(R) ∼= Λ(S) for two finite commutative rings R and S. We also provide a theorem which sa...
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ژورنال
عنوان ژورنال: Journal of Advances in Mathematics and Computer Science
سال: 2020
ISSN: 2456-9968
DOI: 10.9734/jamcs/2020/v35i830316