Let R be a ring with Jacobson radical J (R). Following CNI, a submodule N of a left R-
module RM is said to lie over a summand of M if there exists an idempotent e E End (RM) …

This paper investigates the structure of cyclically pure (or C-pure) projective modules. In
particular, it is shown that a ring R is left Noetherian if and only if every C-pure projective left …

A ring R satisfies the right restricted mi&num condi $ ion {right RMC) if and only if for every
essential right ideal E of R the right R-module R/E is artinian, In view of [3, Theorem 21 a …

In this paper, we introduce and study the pure-direct-projective modules, that is the modules
M every pure submodule A of which with M/A isomorphic to a direct summand of M is a direct …

An R-module M is called almost injective if M is a supplement submodule of every module
which contains M. The module M is called F-almost injective if every factor module of M is …

A ring R is called right bounded if every essential right ideal contains a nonzero two-sided
ideal which is an essential ideal as a right ideal. If R is both right and left bounded, then we …

RIGHT HEREDITARY, RIGHT PERFECT RINGS ARE SEMIPRIMARY Page 1 RIGHT
HEREDITARY, RIGHT PERFECT RINGS ARE SEMIPRIMARY MARK L. TEPLY ABSTRACT. If …

A module M is said to be weakly N-projective if it has a projective cover π: P (M)↠ M and for
each homomorphism: P (M)→ N there exists an epimorphism σ: P (M)↠ M such that (kerσ) …

We shall call a ring R a left IF ring if every injective left R-module is flat. The purpose of this
paper is to characterize left and two-sided IF rings in several ways and to give some …