内射模和投射模的推广

Generalization of injective modules and projective modules

设R是环,n和d是固定的非负整数,T是1-倾斜R-模(未必有限生成).称R-模M是(n,d)-T-内射模,如果对任意P∈Pr esn T,有ExtdR+1(P,M)=0.称R-模M是(n,d)-T-投射模,如果对任意(n,d)-T-内射模N,有Ext1R(M,N)=0.给出(n,d)-T-内射模与(n,d)-T-投射模的若干性质并证明(P Tn,d,I Tn,d)是一个完全的余挠理论,其中P Tn,d,I Tn,d分别表示所有(n,d)-T-投射模组成的类和(n,d)-T-内射模组成的类.

Let R be a ring,n and d fixed non-negative integers,and T was a 1-tilting R-module（not necessarily finitely generated）.An R-module M was called（n,d）-T-injective if Extd＋1R（P,M）=0 for any R-module P∈Pr esnT.R-module M was called（n,d）-T-projective if Ext1R（M,N）=0 for any（n,d）-T-injective R-module N. The paper gave out some properties of（n,d）-T-injective modules and（n,d）-T-projective modules,and it proved that（P Tn,d,I Tn,d） would be a complete co-torsion theory,where P Tn,d and ITn,dwould respectively denote the class of all（n,d）-T-projective module and the class of（n,d）-T-injective module.