n-强Ding分次模

n-Strongly Ding Graded Modules

设G是群,R是G分次环.引入n强Ding分次内(投)射R模的概念,讨论了n强Ding分次内(投)射R模的同调性质.证明了:分次左R模M是n强Ding分次投射模当且仅当存在分次左R模的正合列0→M→P_(n-1)→P_(n-2)→…→P_(0)→M→0,其中Pj(0≤j≤n-1)是分次投射模,并且对任意分次平坦左R模F及任意整数i≥1,Ext^(i)_(R-gr)(M,F)=0.同时,讨论了分次环上的分次模与基础环上模的n强Ding内(投)射性间的联系.

Let G be a group,and R a G-graded ring.The concept of the n-Strongly Ding graded injective(resp.projective)R-modules has been introduced,and the homological properties of the n-Strongly Ding graded injective(resp.projective)R-modules been investigated.It is proved that the modules is a n-Strongly Ding graded projective left R-module if and only if there exists an exact sequence of graded left R-modules 0→M→P_(n-1)→P_(n-2)→…→P_(0)→M→0 with each Pj(0≤j≤n-1)is a graded projective module.And for any graded flat left R-module F and any integer i≥1,Ext^(i)_(R-gr)(M,F)=0.At the same time,the relationship between the graded module on the graded ring and the n-Strongly Ding graded injective(resp.projective)properties on the basic ring are discussed.