The Cotorsion Pair Cogenerated by the Subcategory of Stable Functors in ((R-mod)^op, Ab)  

作　　者：Xianhui Fu Meiyuan Ni 

机构地区：[1]School of Mathematics and Statistics, Northeast Normal University Changchun 130024, China

出　　处：《Algebra Colloquium》2019年第2期259-270,共12页代数集刊（英文版）

基　　金：National Natural Science Foundation of China (No. 11671069).

摘　　要：Let R be an associative ring with identity. Denote by ((R-mod)^op, Ab) the category consisting of contravariant functors from the category of finitely presented left R-modules R-mod to the category of abelian groups Ab. An object in ((R-mod)^op, Ab) is said to be a stable functor if it vanishes on the regular module R. Let T be the subcategory of stable functors. There are two torsion pairs t1=(Gen(-,R),T)and t2=(T,F1), where 1 is the subcategory of ((R-mod)^op, Ab) consisting of functors with flat dimension at most 1. In this article, let R be a ring of weakly global dimension at most 1, and assume R satisfies that for any exact sequence 0 → M → N → K → 0, if M and N are pure injective, then K is also pure injective. We calculate the cotorsion pair (⊥T,(⊥T)⊥)cogenerated by T clearly. It is shown that G∈⊥T if and only if G/t1(G) is a projective object in T, i.e., G/t1(G)=(-,M) for some R-module M;and G∈(⊥T)⊥ if and only if G/t2(G) is of the form (-, E), where E is an injective R-module.

关 键 词：stable FUNCTORS cotorsion PAIRS TORSION PAIRS 

分 类 号：O1[理学—数学]