Zero-divisor graph of matrix rings and Hurwitz rings

Authors : Cihat ABDİOĞLU

Pages : 201-209

View : 9 | Download : 7

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :Let $R$ be ring a with identity $1\neq 0$, $S_ninsert ignore into journalissuearticles values(R);$ be a subring of the ring $T_ninsert ignore into journalissuearticles values(R);$ of $n\times n$ upper triangular matrices over $R$, and $H_ninsert ignore into journalissuearticles values(R);$ be the ring defined in the next section using $HR$, the ring of the Hurwitz series over $R$. In this paper, we introduce the zero-divisor graph $\overset{\rightarrow}{\Gamma}insert ignore into journalissuearticles values(S_ninsert ignore into journalissuearticles values(R););$ and its underlying undirected graph $\Gammainsert ignore into journalissuearticles values(S_ninsert ignore into journalissuearticles values(R););$ of $S_ninsert ignore into journalissuearticles values(R);$. We give some basic graph theory properties of $\overset{\rightarrow}{\Gamma}insert ignore into journalissuearticles values(S_ninsert ignore into journalissuearticles values(R););$. Moreover, we obtain some results of the zero-divisor directed graph of $\overset{\rightarrow}{\Gamma}insert ignore into journalissuearticles values(H_ninsert ignore into journalissuearticles values(R););$.
Keywords : Zero divisor graph, matrix ring, Hurwitz ring