Can I read On Directed Zero-divisor Graphs of Finite Rings on EtoBox?

On Directed Zero-divisor Graphs of Finite Rings by Wu, Tongsuo is a scholarly article available to read on EtoBox.

What is On Directed Zero-divisor Graphs of Finite Rings about?

For an artinian ring $R$, the directed zero-divisor graph $\Gamma(R)$ is connected if and only if there is no proper one-sided identity element in $R$. Sinks and sources are characterized and clarified for finite ring $R$, especially, it is proved that for {\it any} ring $R$, if there exists a source $b$ in $\Gamma(R)$ with $b^2=0$, then $|R|=4$ and $R=\{0,a,b,c\}$, where $a$ and $c$ are left identity elements and $ba=0=bc$. Such a ring $R$ is also the only ring such that $\Gamma (R) $ has exactly one source. This shows that $\Gamma(R)$ can not be a network for any ring $R$.

Author

Wu, Tongsuo

Published

2004

Language

EN