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

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.