Gorenstein正则环上Gorenstein投射覆盖的存在性  

The existence of Gorenstein projective covers over Gorenstein regular rings

作　　者：张豫冈 曹天涯 ZHANG Yu-gang;CAO Tian-ya(Department of Basic Subjects,Lanzhou Institute of Technology,Lanzhou 730050,Gansu,China;College of Computer Science and Engineering,Northwest Normal University,Lanzhou 730070,Gansu,China)

机构地区：[1]兰州工业学院基础学科部,甘肃兰州730050 [2]西北师范大学计算机科学与工程学院,甘肃兰州730070

出　　处：《西北师范大学学报（自然科学版）》2023年第5期35-38,52,共5页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(12161049);甘肃省自然科学基金资助项目(21JR1RA229)。

摘　　要：设R是Gorenstein正则环,给出了所有R-模具有Gorenstein投射覆盖的充要条件.作为应用,给出交换Gorenstein遗传环是Gorenstein Artin代数的新的同调刻画.Let R be a Gorenstein regular ring,some sufficient and necessary conditions that all R-modules have a Gorenstein projective cover are given.As applications,a homological characterization that a commutative Gorenstein hereditary ring is a Gorenstein Artin algebra is given.

关 键 词：Gorenstein正则环 Gorenstein投射覆盖 完全环 GORENSTEIN投射模 Gorenstein遗传环 

分 类 号：O153.3[理学—数学]