Let R be a ring, * be an involutory function of the set of all finite matrices over R. In this paper, necessary and sufficient conditions are given for a matrix to have a (1,3)-inverse, (1,4)-inverse, or Moore-P enros...Let R be a ring, * be an involutory function of the set of all finite matrices over R. In this paper, necessary and sufficient conditions are given for a matrix to have a (1,3)-inverse, (1,4)-inverse, or Moore-P enrose inverse, relative to *. Some results about generalized inverses of matrices over division rings are generalized and improved.展开更多
We study some homological properties of Gorenstein FP∞-injective modules,and we prove(1)a ring R is not necessarily coherent if every Gorenstein FP∞-injective R-module is injective,and(2)a ring R is not necessarily ...We study some homological properties of Gorenstein FP∞-injective modules,and we prove(1)a ring R is not necessarily coherent if every Gorenstein FP∞-injective R-module is injective,and(2)a ring R is not necessarily coherent if every Gorenstein injective R-module is injective.In addition,we characterize w-Noetherian rings in terms of Gorenstein FP∞-injective modules,and we prove that a ring R is w-Noetherian if and only if every GV-torsion-free FP∞-injective R-module is Gorenstein FP∞-injective,if and only if any direct sum of GV-torsion-free FP∞-injective R-modules is Gorenstein FP∞-injective.展开更多
文摘Let R be a ring, * be an involutory function of the set of all finite matrices over R. In this paper, necessary and sufficient conditions are given for a matrix to have a (1,3)-inverse, (1,4)-inverse, or Moore-P enrose inverse, relative to *. Some results about generalized inverses of matrices over division rings are generalized and improved.
基金supported by the Scientific Research Foundation of Chengdu University of Information Technology(No.KYTZ202015)supported by NSFC(No.12061001).
文摘We study some homological properties of Gorenstein FP∞-injective modules,and we prove(1)a ring R is not necessarily coherent if every Gorenstein FP∞-injective R-module is injective,and(2)a ring R is not necessarily coherent if every Gorenstein injective R-module is injective.In addition,we characterize w-Noetherian rings in terms of Gorenstein FP∞-injective modules,and we prove that a ring R is w-Noetherian if and only if every GV-torsion-free FP∞-injective R-module is Gorenstein FP∞-injective,if and only if any direct sum of GV-torsion-free FP∞-injective R-modules is Gorenstein FP∞-injective.
