G_C-同调维数  

G_C-Homological Dimensions

作　　者：方桂英[1] 黄朝凌[1] 

机构地区：[1]江西农业大学理学院,中国南昌330045

出　　处：《湖南师范大学自然科学学报》2012年第1期5-8,共4页Journal of Natural Science of Hunan Normal University

基　　金：江西农业大学自然科学基金资助项目(09003320)

摘　　要：研究GC-同调维数.首先考虑了GC-同调维数与经典同调维数的关系;考虑了GC-投射维数的换环定理,给出了经典第二换环定理的一个推广;定义了任意交换环R的有限GC-投射维数和模的TC-平坦维数,探讨了前者与有限PC-投射维数的关系,后者与模的GC-平坦维数的关系;最后,研究了短正合列GC-同调维数的关系.The GC-homological dimensions are investigated.Firstly,the relation between the GC-homological dimensions and classical homological dimensions is considered.Secondly,the change of rings theorem on GC-projective dimensions is studied.One of classical results is generalized.Thirdly,the notions of finitistic GC-projective dimension FGCPD(R) of the ring R and TC-flat dimension TC-fdR(M) of R-module M are given.It is proved that FGCPD(R)=FPCD(R) and TC-fdR(M) ≤GC-fdR(M).Finally,the ralation of GC-homological dimensions of short exact sequence is investigated.

关 键 词：同调维数 Gc-投射模 Pc-内射模 换环定理 

分 类 号：O15[理学—数学]