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

Year 2013, Volume: 14 Issue: 14, 32 - 43, 01.12.2013

Zhanmin Zhu

Abstract

Let M be a right R-module with S = End(MR). Then MR is
called pseudo QP-injective (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 (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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• Department of Mathematics Jiaxing University Jiaxing, Zhejiang Province, P.R.China e-mail: zhanmin [e-mail]