## On simple singular GP-injective modules.(English)Zbl 0923.16008

A right $$R$$-module $$M$$ is called generalized right principally injective (simply right GP-injective) if, for any $$0\neq a\in R$$, there exists a positive integer $$n=n(a)$$ depending on $$a$$ such that $$a^n\neq 0$$ and any right $$R$$-homomorphism from $$a^nR$$ to $$M$$ extends to one of $$R$$ to $$M$$.
Von Neumann regularity of rings whose simple singular $$R$$-modules are GP-injective is investigated. It is proved that a ring $$R$$ is strongly regular if and only if $$R$$ is a weakly right duo ring whose simple singular right $$R$$-modules are GP-injective. Also it is shown that a ring $$R$$ is either a strongly right bounded ring or a zero insertive ring in which simple singular right $$R$$-modules are GP-injective is reduced weakly regular.
Reviewer: J.K.Park (Pusan)

### MSC:

 16E50 von Neumann regular rings and generalizations (associative algebraic aspects) 16D50 Injective modules, self-injective associative rings 16D60 Simple and semisimple modules, primitive rings and ideals in associative algebras
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