关于n-Ding同调模

On n-Ding Homological Modules

引入n-Ding同调模,统一了Gorenstein同调模、Ding同调模和Gorenstein AC同调模的概念.讨论了n-Ding同调模的诸多性质,例如n-Ding投射模类是投射可解的,n-Ding内射模类是内射可解的.证明了当n>1时,n-Ding投射模是n-Ding平坦模,特别地,Gorenstein AC投射模是Gorenstein AC平坦模.最后,用n-Ding同调模刻画了一些熟知的环类,如:Noether环、完全环、QF环、FC环等,补充了Gorenstein同调理论的相关研究结果.

The concept of n-Ding homology modules is introduced,which unifies the concepts of Gorenstein homology modules,Ding homology modules and Gorenstein AC homology modules.Some properties of n-Ding homology modules are discussed.For example,the class of n-Ding projective modules is projectively resolving and the class of n-Ding injective modules is injectively resolving.It is proved that every n-Ding projective module is n-Ding flat when n>1,in particular,every Gorenstein AC-projective module is Gorenstein AC-flat.Furthermore,some characterizations of rings in terms of n-Ding homology modules are discussed.Some well-known rings such as Noetherian rings,perfect rings,QF rings and FC rings are characterized,which complements the related research results in Gorenstein homology theory.