A ring R is called left nil-injective if every R-homomorphism from a principal left ideal which
is generated by a nilpotent element to R is a right multiplication by an element of R. In this …

A ring R is called left P-injective if for every a∈ R, aR= r (l (a)) where l (⋅) and r (⋅) denote
left and right annihilators respectively. The ring R is called left GP-injective if for any 0≠ a∈ …

Rings in which certain right ideals are direct summands of annihilators Page 1 J. Aust. Math.
Soc. 73 (2002), 335-346 RINGS IN WHICH CERTAIN RIGHT IDEALS ARE DIRECT …

A ring R is called left NP P if for any nilpotent element a of R, l (a)= Re, e2= e∈ R. A right R−
module M is called N f lat if for each a∈ N (R), the Z− module map 1M⊗ i: M⊗ R Ra−→ M⊗ …

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Let M and N be right R-modules. Hom (M, N) is called regular if for each f∈ Hom (M, N),
there exists g∈ Hom (N, M) such that f= fgf. Let [M, N]= Hom R (M, N). We prove that if M is …

In this paper, we extend some results of V rings to GP-V rings and GP-V'rings. Some
characterizations of strongly regular rings are obtained. We show that (1) R is strongly …

In this article, the notion of pure hereditary rings is introduced as a nontrivial generalization
of the notion of both pure semisimple rings and of hereditary rings. Some properties and …

In this article, we call a ring R right generalized semiregular if for any a∈ R there exist two
left ideals P, L of R such that lr (a)= P⊕ L, where P⊆ Ra and Ra∩ L is small in R. The class …

A ring R is said to be right MP-injective if every monomorphism from a principal right ideal to
R extends to an endomorphism of R. A ring R is said to be right MGP-injective if, for any 0≠ …