TY - JOUR
ID - 1781
TI - On zero-divisor graphs of quotient rings and complemented zero-divisor graphs
JO - Journal of Algebra and Related Topics
JA - JART
LA - en
SN - 2345-3931
AU - Karimi Beiranvand, P.
AU - Beyranvand, R.
AD - Islamic Azad university,
Khorramabad Branch, Khorramabad
AD - Lorestan University
Y1 - 2016
PY - 2016
VL - 4
IS - 1
SP - 39
EP - 50
KW - Quotient ring
KW - zero-divisor graph
KW - reduced ring
KW - complemented graph
DO -
N2 - 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 paper we extend this fact for certain noncommutative rings, for example, reduced rings, right (left) self-injective rings and one-sided Artinian rings. The necessary and sufficient conditions for two reduced right Goldie rings to have isomorphic zero-divisor graphs is given. Also, we extend some known results about the zero-divisor graphs from the commutative to noncommutative setting: in particular, complemented and uniquely complemented graphs.
UR - https://jart.guilan.ac.ir/article_1781.html
L1 - https://jart.guilan.ac.ir/article_1781_38d9e44bdeda75362869943f4e3b1c63.pdf
ER -