Throughout this paper, R denotes an associative ring with identity and all modules are
unitary. A right R-module M is called principally injective briefly, p-injective) if for any …

Throughout this paper R denotes associative with identity and all modules are unitary. J (R)
and Z,(R) denote the Jacobson radical and the singular right ideal of R, respectively. A right …

For a left uniserial ring R, Nicholson and Yousif proved that R is right p-injective if and only if
J (R)= Z [subr](R). Later on, Puninski, Wisbauer and Yousif characterized right p-injectivity …

1. Introduction In [5], Nicholson and Yousif called a ring R right principallv in iective (P-in.
jective) if every R-ho~ nomorphism from a principal right ideal to 11 is left multiplication by …

A ring R is called left IP-injective if every homomorphism from a left ideal of R into R with
principal image is given by right multiplication by an element of R. It is shown that R is left IP …

A ring R is called right-right (resp. right-left) weakly P-injective, if, for any 0≠ a∈ R, there
exists b∈ R such that ba∈ 0 (resp. ab≠ 0) and any right R-homomorphism from baR (resp …

We investigate characterizations of rings whose simple singular right R-modules are GP-
injective. It is proved that if R is a semiprime ring whose simple singular right R-modules are …

The following results are extended fromP-injectiverings to AP-injective rings:(1) R is left self-
injective regular ifand only if R is a right (resp. left) AP-injective ring such that forevery nitely …

Let R be a ring and M a right R-module with S= end (M< sub> R). Then M is called general
quasi-injective (briefly GQP-injective) if for any 0≠ s∈ S, there exists a positive integer n …

A right ideal I of a ring R is small in case for every proper right ideal K of R, K+ I ${\neq} $= R.
A right R-module M is called PS-injective if every R-homomorphism f: aR ${\rightarrow} $ M …