非诣零P-内射模及其应用  

Nonnil P-injective Modules and Their Applications

作　　者：张晓磊 齐薇 ZHANG Xiaolei;QI Wei(School of Mathematics and Statistics,Shandong University of Technology,Zibo,Shandong,255000,P.R.China)

机构地区：[1]山东理工大学数学与统计学院,山东淄博255000

出　　处：《数学进展》2024年第6期1210-1216,共7页Advances in Mathematics（China）

基　　金：国家自然科学基金(Nos.12201361,12061001)。

摘　　要：设R是交换环及M是R-模.若对任意非幂零元素a∈R都有Ext_(R)^(1)(R/Ra,M)=0,则称M为非诣零P-内射模.本文研究了非诣零P-内射模的盖包性质,并用非诣零P-内射模刻画了Φ-von Neumann正则环、整环、ZN-环和Φ-Dedekind环等环类.Let R be a commutative ring and M be an R-module.If Ext_(R)^(1)(R/Ra,M)=0 for any non-nilpotent element a∈R,then M is said to be nonnil P-injective.We study the enveloping and covering properties of nonnil P-injective modules,and then characterizeΦ-von Neumann regular rings,integer domains,ZN-rings andΦ-Dedekind rings in terms of nonnil P-injective modules.

关 键 词：非诣零P-内射模 Φ-von Neumann正则环 ZN-环 Φ-Dedekind环 

分 类 号：O153.3[理学—数学]