ZWGP-内射性与环的非奇异性

doi:10.6040/j.issn.1671-9352.0.2016.173

山东大学学报（理学版） ›› 2017, Vol. 52 ›› Issue (2): 19-23.doi: 10.6040/j.issn.1671-9352.0.2016.173

ZWGP-内射性与环的非奇异性

鲁琦,鲍宏伟

蚌埠学院数学与物理系, 安徽蚌埠 233030

收稿日期:2016-04-21 出版日期:2017-02-20 发布日期:2017-01-18
作者简介:鲁琦(1980— ),男,硕士,讲师,研究方向为代数学.E-mail:luqi19801124@163.com
基金资助:
国家自然科学基金资助项目(11271016);安徽省自然科学基金资助项目(KJ2012Z300);蚌埠学院自然科学基金资助项目(2015ZR10)

ZWGP-injectivity and nonsingularity of rings

LU Qi, BAO Hong-wei

Department of Mathematics and Physics, Bengbu University, Bengbu 233030, Anhui, China

Received:2016-04-21 Online:2017-02-20 Published:2017-01-18

摘要/Abstract

摘要： 引入了ZWGP-内射模和ZWGP-内射环的概念,对ZWGP-内射环进行了等价刻画。研究了ZWGP-内射模(环)的性质,举例说明了ZWGP-内射环和非奇异环的关系。给出了环是非奇异的充分必要条件。证明了:(1)若环R的左零化子是R的W-理想,且R的任意本质理想均是左ZWGP-内射的,则R是左非奇异环;(2)若对R的任意本质左理想I,R/I是ZWGP-内射的,且l(a1)⊆l(a1a2)⊆l(a1a2a3)⊆…是平稳的, a_i∈Z(_RR),i=1,2,3,…,则R是左非奇异的。

关键词: ZWGP-内射模, 非奇异环, WGP-内射环, GP-内射环, ZWGP-内射环

Abstract: ZWGP-injective modules and ZWGP-injective rings are introduced; equivalent characterizations of ZWGP-injective rings are obtained. The properties of ZWGP-injective modules(rings)are explored, the relations between ZWGP-injective rings and nonsingular rings are illustrated by some examples, and sufficient and necessary conditions that rings are nonsingular are given. It is proved that:(1)If left annihilators of R are W-ideals of R, and any essential ideals of R are left ZWGP-injective, then R is left nonsingular;(2)If for any essential left ideal I,R/I is ZWGP-injective, and l(a1)⊆l(a1a2)⊆l(a1a2a3)⊆… is stable, a_i∈Z(_RR), i=1,2,3,…, then R is left nonsingular.

Key words: WGP-injective ring, ZWGP-injective module, ZWGP-injective ring, GP-injective ring, nonsingular ring

中图分类号:

O153.3

鲁琦,鲍宏伟. ZWGP-内射性与环的非奇异性[J]. 山东大学学报（理学版）, 2017, 52(2): 19-23.

LU Qi, BAO Hong-wei. ZWGP-injectivity and nonsingularity of rings[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 19-23.

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ZWGP-内射性与环的非奇异性

ZWGP-injectivity and nonsingularity of rings

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