Ext_F-投射生成子与Ext_F-内射余生成子  

Ext_F-Projective Generators and Ext_F-Injective Cogenerators

作　　者：张春霞 刘仲奎 ZHANG Chunxia;LIU Zhongkui(Corresponding author.School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China;Department of Mathematics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]重庆师范大学数学科学学院 [2]西北师范大学数学与统计学院

出　　处：《数学年刊（A辑）》2018年第4期407-428,共22页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11261050;No.11401475);重庆市科技计划项目(No.cstc2017jcy jAX0298)的资助

摘　　要：设A是Abel范畴,F是Ext_A^1(-,-):A^(op)×A→A的加法子双函子.首先研究了Ext_(F-)投射生成子与Ext_F-内射余生成子的同调性质,其次引入了W_F-Gorenstein模的概念.特别地,证明了如果重复W_F-Gorenstein模的定义程序将不会产生新的模类.最后,统一并推广了许多参考文献中的结论.Let A be an abelian category,F be an additive subbifunctor of the additive bifunctor Ext^1A(-,-):Aop ×A→A.This paper deals with the homological properties of ExtF-projective generators and ExtF-injective cogenerators.As a consequence,an iteration of the procedure is used to define the WF-Gorenstein modules over a ring R yields exactly the WF-Gorenstein modules.Many results are unified and naturally generalized.

关 键 词：ExtF-投射生成子 ExtF-内射余生成子 F-可解子范畴 F-余可解子范畴 WF-Gorenstein模 

分 类 号：O153.3[理学—数学]