关于一类模范畴的反变有限性(英文)

On contravariant finiteness of certain subcategories in the category of modules over an algebra

设Λ是一个Artin代数,Λ-mod表示有限生成的左Λ-模范畴,所有投射维数有限的Λ-模做成的Λ-mod的满子范畴记为∞(Λ).设T∈Λ-mod,定义Λ-mod的满子范畴(T)={M∈Λ-mod存在一个正合列Tn→M→0,n∈Z}+∩∞(Λ).研究了子范畴(T)在Λ-mod中反变有限的问题,通过对Λ-模T的结构上的适当构造,得到了两种情形下(T)在Λ-mod中是反变有限的.

Let Λ be an Artin algebra and Λ-mod the category of all left finitely generated Λ-modules.The subcategory consisting of all Λ-modules of finite projective dimension is denoted by P∞（Λ）.Let T be a Λ-module,and G（T）={M∈Λ-mod then there exists an exact sequence Tn→M→0,n∈Z＋}∩P∞（Λ）as a full subcategory of Λ-mod.This article discusses the problem on contravariant finiteness of G（T）in Λ-mod by constructing a Λ-module T.In two cases,we conclude G（T）is contravariantly finite in Λ-mod.