【作者】 魏玉娟；

【导师】 张文汇；

【作者基本信息】 西北师范大学 ， 基础数学， 2023， 硕士

【摘要】 本文主要讨论了两类复形,FC-投射复形和Gorenstein FC-投射复形,研究了这两类复形的基本同调性质.首先,我们给出FC-投射复形结构的刻画,证明了复形C是FC-投射复形当且仅当每个层次上的模都是FC-投射模,并且对任意有限余表示复形Q,复形Hom(C,Q)正合;进一步证明了 FC-投射复形是一类正合复形;其次,我们证明了复形C是Gorenstein FC-投射复形当且仅当每个层次上的模都是Gorenstein FC-投射模,并且对任意FC-投射复形M,复形Hom(C,M)正合;最后,我们引入并讨论了复形的Gorenstein FC-投射维数.更多还原

【Abstract】 In this paper,two classes of complexes are discussed,which are called FCprojective complexes and Gorenstein FC-projective complexes respectively.Some homological properties of these classes are investigated.Firstly,we give the structural characterization of the FC-projective complexes,and prove that a complex C is FCprojective complexes if and only if Cn is FC-projective modules for all n ∈ Z,and Hom(C,Q)is exact for all finitely copresented complexes Q;It is further prove that the FC-projective complexes is a kind of exact complexes.Secondly,we prove that a complex C is Gorenstein FC-projective complexes if and only if Ci is Gorenstein FC-projective modules for all i ∈ Z,and Hom(C,M)is exact for all FC-projective complexes M;Finally,the Gorenstein FC-projective dimension of complexes are introduced and discussed.更多还原