FI-gr-内射模

doi:10.16088/j.issn.1001-6600.2019.01.018

Abstract

Abstract: In this paper, the notions of FI-gr-injective modules and strongly FI-gr-injective modules are introduced, and the relationship between them and graded injective modules is explained. It is proved that the graded ring R is a gr-QF ring if and only if each graded module is a strongly FI-gr-injective module; suppose R is a left gr-coherent ring, then l.FP-gr-dim(R)≤1 if and only if each FI-gr-injective module is a graded injective module. In addition, it is also proved that l.gr-fiD(R)=sup{gr-pd(L)|L is an FP-gr-injective module}.

Key words: FI-gr-injective modules, strongly FI-gr-injective modules, FI-gr-injective dimensions, FP-gr-injective modules

CLC Number:

O154

LIU-TIAN Lilian , WANG Fanggui, GAO Zenghui. FI-gr-injective Modules[J].Journal of Guangxi Normal University(Natural Science Edition), 2019, 37(1): 155-164.

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