Zero-divisor Graphs for Direct Products of Rings

Chinese Quarterly Journal of Mathematics ›› 2011, Vol. 26 ›› Issue (4): 621-627.

Zero-divisor Graphs for Direct Products of Rings

1. Yuan'an No.1 Senior High School2. Department of Mathematics, Guangxi Teacher's College

Received:2009-12-10 Online:2011-12-30 Published:2023-04-17
About author:LI Yun-hui(1977-), female, native of Yichang, Hubei, a teacher of Yuan’an Senior Middle School, M.S.D., engages in commuatative algebra; TANG Gao-hua(1965-), male, native of Guilin, Guangxi, a professor of Guangxi Teacher’s College, Ph.D., engages in homological algebra.
Supported by:
Supported by the Natural Sciences Foundation of Guangxi Province(0575052, 0640070)； Supported by the Innovation Project of Guangxi Graduate Education(2006106030701M05)； Supported by the Scientific Research Foundation of Guangxi Educational Committee(200707LX233；

Abstract

Abstract: In [1], Joe Warfel investigated the diameter of a zero-divisor graph for a direct product R₁×R₂ with respect to the diameter of the zero-divisor graph of R₁and R₂. But the author only considered those graphs whose diameters ≥ 1 and discussed six cases. This paper further discusses the other nine cases and also gives a complete characterization for the possible diameters for left Artin rings.

Key words: zero-divisor graph, diameter, Artin ring, local ring

CLC Number:

O153.3

LI Yun-hui, TANG Gao-hua. Zero-divisor Graphs for Direct Products of Rings[J]. Chinese Quarterly Journal of Mathematics, 2011, 26(4): 621-627.

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Zero-divisor Graphs for Direct Products of Rings

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