Turkish Journal of Mathematics
DOI
10.3906/mat-1505-51
Abstract
Let $R$ be ring a with identity $1\neq 0$, $S_n(R)$ be a subring of the ring $T_n(R)$ of $n\times n$ upper triangular matrices over $R$, and $H_n(R)$ 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 $\overset{\rightarrow}{\Gamma}(S_n(R))$ and its underlying undirected graph $\Gamma(S_n(R))$ of $S_n(R)$. We give some basic graph theory properties of $\overset{\rightarrow}{\Gamma}(S_n(R))$. Moreover, we obtain some results of the zero-divisor directed graph of $\overset{\rightarrow}{\Gamma}(H_n(R))$.
Keywords
Zero-divisor graph, matrix ring, Hurwitz ring
First Page
201
Last Page
209
Recommended Citation
ABDİOĞLU, CİHAT
(2016)
"Zero-divisor graph of matrix rings and Hurwitz rings,"
Turkish Journal of Mathematics: Vol. 40:
No.
1, Article 18.
https://doi.org/10.3906/mat-1505-51
Available at:
https://journals.tubitak.gov.tr/math/vol40/iss1/18
