PSEUDO QP-INJECTIVE MODULES AND GENERALIZED PSEUDO QP-INJECTIVE MODULES

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International Electronic Journal of Algebra
Volume:14 Issue:14
PSEUDO QP-INJECTIVE MODULES AND GENERALIZED PSEUDO QP-INJECTIVE MODULES

PSEUDO QP-INJECTIVE MODULES AND GENERALIZED PSEUDO QP-INJECTIVE MODULES

Authors : Zhanmin ZHU

Pages : 32-43

View : 38 | Download : 11

Publication Date : 2013-12-01

Article Type : Research Paper

Abstract :Let M be a right R-module with S = Endinsert ignore into journalissuearticles values(MR);. Then MR is called pseudo QP-injective insert ignore into journalissuearticles values(or P QP-injective for short); if every monomorphism from an M-cyclic submodule of M to M extends to an endomorphism of M . MR is called generalized pseudo QP-injective insert ignore into journalissuearticles values(or GP QP-injective for short); if, for any 0 6= s ∈ S, there exists a positive integer n such that s n 6= 0 and every monomorphism from snM to M extends to an endomorphism of M. Characterizations and properties of the two classes of modules are studied. The two classes of modules with some additional conditions are studied, semisimple artinian rings are characterized by P QP-injective modules.
Keywords : P QP injective modules, GP QP injective modules, endomorphism rings, semisimple artinian rings, perfect rings

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