Gorenstein X-内射复形类的稳定性

Stability of Gorenstein X-injective Complexes

定义了Gorenstein X-内射复形,证明了Gorenstein X-内射复形的稳定性。设X∈C(R),则X是Gorenstein X-内射复形当且仅当存在HomC(R)(XJ,G)正合的Gorenstein X-内射复形的正合序列G=…→G1σ1→G0σ0G-1σ-1→G-2→…,使得X≌Ker(σ-1),其中XJ是X-内射复形类。

In this paper,Gorenstein X-injective complexes are introduced and studied.A complex X is recalled Gorenstein X-injective complexes only and if only there is a HomCR(XI,G)exact exact sequence G=…→G1σ1→G0σ0G-1σ-1→G-2→…of Gorenstein X-injective complexes such that X≌Ker(σ-1),where XIstands for the class of all X-injective complexes.