Frobenius函子和Gorenstein投射预覆盖  

Frobenius Functors and Gorenstein Projective Precovers

作　　者：胡江胜[1,2] 李欢欢 吕家凤 张东东[1] HU Jiangsheng;LI Huanhuan;LÜ Jiafeng;ZHANG Dongdong(Department of Mathematics,Zhejiang Normal University,Jinhua,Zhejiang,321004,P.R.China;School of Mathematics and Physics,Jiangsu University of Technology,Changzhou,Jiangsu,213001,P.R.China;School of Mathematics and Statistics,Xidian University,Xi'an,Shaanxi,710071,P.R.China)

机构地区：[1]浙江师范大学数学系,金华浙江321004 [2]江苏理工学院数理学院,常州江苏213001 [3]西安电子科技大学数学与统计学院,西安陕西710071

出　　处：《数学进展》2022年第4期687-694,共8页Advances in Mathematics（China）

基　　金：supported by NSFC (Nos.11671069,11771212);Qing Lan Project of Jiangsu Province and Jiangsu Government Scholarship for Overseas Studies (No.JS-2019-328);supported by NSFC (No.11626179);Shaanxi Province Basic Research Program of Natural Science (No.2017JQ1012);supported by NSFC (No.11571316);Natural Science Foundation of Zhejiang Province (No.LY16A010003)。

摘　　要：为研究任意环上的每个模是否存在Gorenstein投射预覆盖这一公开问题,我们利用Frobenius函子建立了Gorenstein投射预覆盖之间的关系.本文证明:如果F:C→D是有足够多投射对象的Abel范畴之间的可分Frobenius函子且D中每个对象都存在Gorenstein投射预覆盖,那么C中每个对象也存在Gorenstein投射预覆盖.这个结果可应用在可分Frobenius环扩张和优越环扩张上.We establish relations between Gorenstein projective precovers linked by Frobenius functors.This is motivated by an open problem that how to find general classes of rings for which modules have Gorenstein projective precovers.It is shown that if F:C→D is a separable Frobenius functor between abelian categories with enough projective objects,then every object in C has a Gorenstein projective precover provided that every object in D has a Gorenstein projective precover.This result is applied to separable Frobenius extensions and excellent extensions.

关 键 词：Frobenius函子 Gorenstein投射对象 预覆盖 

分 类 号：O154.2[理学—数学]