GV-挠理论所确定的投射性质  

On the Projectivity Induced by GV-torsion Theories

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5期1003-1011,共9页Advances in Mathematics（China）

基　　金：国家自然科学基金(No.12201361)。

摘　　要：本文引入GV-投射模和弱GV-投射模,研究其基本性质,并给出DW-环和半单环等环类的新刻画.定义一致GV-挠模为存在GV-理想J满足JT=0的R-模T,并将GV-投射模(弱GV-投射模)定义为Hom_R(P,-)保持核为GV-挠模(一致GV-挠模)的满同态的R-模P.首先得到环R是DW-环当且仅当任意R-模都是GV-投射模,当且仅当任意R-模都是弱GV-投射模.其次证明环R是半单环当且仅当任意弱GV-投射模都是投射模.最后推出任意弱GV-投射模都是GV-平坦模.此外,给出一些例子来区分GV-投射模、弱GV-投射模、w-投射模和GV-平坦模.The main purpose of this paper is to introduce the notion of GV-projective modules and weak GV-projective modules,investigate their basic properties,and then give some new characterizations of DW-rings and semisimple rings etc.An R-module T is said to be a uniformly GV-torsion module if JT=0 for some GV-ideal J,and an R-module P is said to be GV-projective(resp.,weak GV-projective) if Hom_R(P,-) keeps the epimorphisms with kernel GV-torsion(resp.,uniformly GV-torsion).A ring R is a DW-ring if and only if every GV-torsion module is uniformly,if and only if every R-module is GV-projective if and only if every R-module is weak GV-projective;a ring R is semisimple if and only if every weak GV-projective module is projective;GV-projective modules are GV-flat for all rings.In addition,some examples are given to distinguish GV-projective modules,weak GV-projective modules,w-projective modules and GV-flat modules.

关 键 词：GV-投射模 弱GV-投射模 一致GV-挠模 半单环 DW-环 

分 类 号：O154.2[理学—数学]