微分模的Gorenstein投射和内射复形

Gorenstein Projective and Injective Complexes of Differential Modules

摘要: 考虑微分模的Gorenstein同调理论,证明了一个微分模复形C:=((C_n,θ_n),d_n)是Gorenstein投射的(或Gorenstein内射的)当且仅当每个层次的微分模(C_n,θ_n)都是Gorenstein投射的(或Gorenstein内射的),并且给出了微分模复形的Gorenstein投射维数和Gorenstein内射维数的刻画.

Abstract: Based on the Gorenstein homological theory of differential modules,that a complex C:=((Cⁿ,θⁿ),dⁿ) is Gorenstein projective(resp.Gorenstein injective) if and only if every differential module(Cⁿ,θⁿ) is Gorenstein projective(resp.Gorenstein injective) was proved,and a description of Gorenstein projective dimension and Gorenstein injective dimension of the complex of differential modules was given.