相对FP-内射模

Relative FP-injective Module

给出了n-FP-内射模的定义,讨论了该模类的左维数、(预)覆盖等问题,并主要证明了该模类在左凝聚环的条件下的一些等价关系,如l.FPn-dim(R)≤n等价于对每个0-FP-内射左R-模有id(M)≥n,等价于对每个n-FP-内射左R-模有fpd(M)≤n等;最后给出了n-FP-内射模的维数的定义和性质,并讨论了该模类在左凝聚环的条件下的一些等价关系,如FPn-inj.dim(M)≤n时等价于在有限表示模N∈FPn下,有Extn+1(N,M)=0等。

Abstract： This paper gave the definition of the n-FP-injective module,discussed the left dimension and （pre） cover of this module. It mainly proved some equivalent relation of the category on the left coherent rings. For ex-ample,l. FP-dim（R）≤n and id（M）≤n of every O-FP-injeetive left R-module are equivalent,and it equivalent to fpd（M）≤n. Finally ,it showed the definition of n-FP-injective module and property of its dimension,and also discussed its equivalent relation on the left coherent rings. For instance,finite represent module N∈ FP.,in the case,Extn^＋1（N,M）=0 is equivalent to FPn-inj. dim（M）≤n.