有限生成G-投射模的张量积  

The Tensor Products of Finitely Generated Gorenstein Projective Modules

作　　者：王芳贵[1] 

机构地区：[1]四川师范大学数学与软件科学学院,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2015年第1期1-7,共7页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然基金(11171240);教育部博士点专项科研基金(20125134110002)资助项目

摘　　要：设R是交换环,M,E,N是R-模.称M为超G-余模,是指存在正合列0→M→G0→G1→…→Gm→…,其中每一Gi是超有限表现Gorenstein投射模;称E为GP-内射模,是指对任何超G-余模M,有Ext1R(M,E)=0.用GP-idRN≤n表示对任何超G-余模M,有Extn+1R(M,N)=0.证明了若GP-idRR<∞,A,B是超有限表现G-投射模,且对任何i>0,ExtiR(A,B*)=0,则ARB是超有限表现G-投射模.Let R be a commutative ring. An R-module M is called super Gorenstein cofinitely presented if there is an exact sequence 0→ M→ G0→ G1→ …→ Gm→… in which every Giis a super finitely presented Gorenstein projective module. An R-module E is called a GP-injective module if ExtR^1（M,E） = 0 for all super Gorenstein cofinitely presented module M. An R-module N is said to have GP-injective dimension at most N if ExtR^n ＋ 1（M,N） = 0 for all super Gorenstein cofinitely presented module M. In this paper it is shown that if GP-idRR 〈∞ and if A and B are super finitely presented modules with ExtR^i（A,B^＊） = 0 for all i 〉0,then ARB is super finitely presented Gorenstein projective.

关 键 词：超有限表现模 超G-余模 GP-内射模 GP-内射维数 GORENSTEIN投射模 

分 类 号：O153.3[理学—数学] O154[理学—基础数学]