Let R be a ring. A right R-module N is called an Mp-injective module if any homomorphism
from an M-cyclic submodule of M can be extended to M. In this paper, we extend this notion …

We show that the left pure semisimplicity of a left artinian ring can be characterized by the
contravariant finiteness of subcategories of finitely generated left R-modules. Various …

Given a radical ideal in a regular ring, the Containment Problem of symbolic and ordinary
powers of consists of determining when the containment holds. By work of Ein–Lazersfeld …

Let R be a regular ring. By ΞFwe denote the family of all essentially K0-generated essential
right ideals of R. It is shown that£ F becomes a right Gabriel topology on R (Proposition 5) …

In a series of recent papers, Beidar, Jain and Srivastava studied the question as to when a
ring R with the property that essential extensions of semi-simple right R-modules are direct …

In this paper, we consider the N-pure notion. An ideal $ I $ of a ring $ R $ is said to be N-
pure, if for every $ a\in I $ there exists $ b\in I $ such that $ a (1-b)\in N (R) $, where N (R) is …

A class C of modules over a unitary ring is said to be socle fine if whenever M, N∊ C with
Soc (M)≅ Soc (N) then M≅ N. In this work we characterize certain types of rings by requiring …

Introduction and Notation. A ring R is called a (von Neumann) regular ring if for each a in R
there exists an x in R such that a= axa. The notion of regularity has been extended to …

Let R be a ring. A left R-module M (resp. right R-module N) is called singly injective (resp.
singly flat) if Ext1 (F/C, M)= 0 (resp. Tor1 (N, F/C)= 0) for any cyclic submodule C of any …

We shall introduce the notion of uniformly classical primary submodule that generalizes the
concept of uniformly primary ideal as given by JA Cox and AJ Hetzel. We also advance the …