替换环什么时候是冯诺依曼正则环

doi:10.13371/j.cnki.chin.q.j.m.2019.01.003

数学季刊 ›› 2019, Vol. 34 ›› Issue (1): 21-28.doi: 10.13371/j.cnki.chin.q.j.m.2019.01.003

替换环什么时候是冯诺依曼正则环

College of Mathematics and Computer Science,Hanjiang Normal Universtiy

接受日期:2016-12-30 出版日期:2019-03-30 发布日期:2020-10-06
作者简介:HUANG Chao-ling, male, native of Xiangyang Hubei, Doctor, major in Homological Algebra and Algebraic K-theory.
基金资助:
supported by the guidance project of scientific research plan of Educational Adminstration of Hubei Province,China(B2016162)； the plan of science and technology innovation team of excellent young and middle-age of Hubei province(T201731)；

When Exchange Rings are Von Neumann Regular

College of Mathematics and Computer Science,Hanjiang Normal Universtiy

Accepted:2016-12-30 Online:2019-03-30 Published:2020-10-06
About author:HUANG Chao-ling, male, native of Xiangyang Hubei, Doctor, major in Homological Algebra and Algebraic K-theory.
Supported by:
supported by the guidance project of scientific research plan of Educational Adminstration of Hubei Province,China(B2016162)； the plan of science and technology innovation team of excellent young and middle-age of Hubei province(T201731)；

摘要/Abstract

摘要： We study when exchange rings are von Neumann regular. An exchange ring R with primitive factors Artinian is von Neumann regular, if the Jacobson radical of any indecomposable homomorphic image of R is T-nilpotent, and if any indecomposable homomorphic image of R is semiprime. Every indecomposable semiprimitive factor ring of R is regular, if R is an exchange ring such that every left primitive factor ring of R is a ring of index at most n and if R has nil-property.

关键词: exchange ring, von Neumann regular ring, strong ?-regular ring

Abstract: We study when exchange rings are von Neumann regular. An exchange ring R with primitive factors Artinian is von Neumann regular, if the Jacobson radical of any indecomposable homomorphic image of R is T-nilpotent, and if any indecomposable homomorphic image of R is semiprime. Every indecomposable semiprimitive factor ring of R is regular, if R is an exchange ring such that every left primitive factor ring of R is a ring of index at most n and if R has nil-property.

Key words: exchange ring, von Neumann regular ring, strong ?-regular ring

中图分类号:

O153.3

黄朝凌. 替换环什么时候是冯诺依曼正则环[J]. 数学季刊, 2019, 34(1): 21-28.

HUANG Chao-ling. When Exchange Rings are Von Neumann Regular[J]. Chinese Quarterly Journal of Mathematics, 2019, 34(1): 21-28.

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替换环什么时候是冯诺依曼正则环

When Exchange Rings are Von Neumann Regular

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