直积的零因子图

数学季刊 ›› 2011, Vol. 26 ›› Issue (4): 621-627.

直积的零因子图

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

收稿日期:2009-12-10 出版日期:2011-12-30 发布日期:2023-04-17
作者简介: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.
基金资助:
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；

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；

摘要/Abstract

摘要： 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.

关键词: zero-divisor graph, diameter, Artin ring, local ring

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

中图分类号:

O153.3

李云慧, 唐高华. 直积的零因子图[J]. 数学季刊, 2011, 26(4): 621-627.

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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