%0 Journal Article
%A PAN Hong-Yan
%A LI Ai-Hua
%T Zero-Divisor Graph of Von Neumann Regular Rings
%D 2016
%R 10.3969/j.cnki.jdxb.2016.01.003
%J Journal of Jishou University(Natural Sciences Edition)
%P 11-13
%V 37
%N 1
%X In this paper we investigate the zero-divisor graph of von Neumann regular rings，and we focus our main attention on the property of vertices and the connectedness of the zero-divisor graph Γ(R).Let R be a von Neumann regular ring with unit 1，we show that Γ(R) is connected if and only if R is direct finite.In addition，if R is a regular ring without unity elements，then Γ(R) is connected if and only if R has no proper one-sided identity elements.For the zero-divisor graph Γ(R) of a regular ring R with |R|≥ 5，we have that Sour(R)={a∈R|a is right invertible but not left invertible} and Sink (R)={a∈R|a is left invertible but not right invertible}.
%U https://zkxb.jsu.edu.cn/EN/10.3969/j.cnki.jdxb.2016.01.003