A ring R is called left AIP if R modulo the left annihilator of any ideal is flat. In this paper, we
characterize a module MR for which the endomorphism ring E nd R (M) is left AIP. We say a …

A module M is said to be FI-extending if every fully invariant submodule of M is essential in a
direct summand of M. A ring R is right FI-extending if every ideal of R is right essential in an …

Let R be a ring, S a multiplicative subset of R and M a left R-module. We say M is a weakly S-
Artinian module if every descending chain N1 N2 N3... of submodules of M is weakly S …

The study of the endomorphism rings of modules and connections between a module and its
endomorphism ring have long been of interest. Of particular interest has been a quest of …

The notion of semi-Artinian module, here introduced, is completely different from that of
[1](see our definition in § 2). Throughout this paper all modules are assumed to be unitary …

Abstract Baer's Criterion for Injectivity is a useful tool of the theory of modules. Its dual
version (DBC) is known to hold for all right perfect rings, but its validity for the non-right …

Let M_R be a right R-module. We introduce the concept of right generalized pq-Baer
modules (or simply, right GPQ modules) to extend the notion of right pq-Baer modules. We …

It is well known that the Rickart property of rings is not a left-right symmetric property. We
extend the notion of the left Rickart property of rings to a general module theoretic setting …

Throughout this paper R denotes an associative ring with unity. Recall from [Ka2) that R is a
Baer ring if the right annihilator of every nonempty subset of R is generated, as a right ideal …

The concepts of strongly lifting modules and strongly dual Rickart modules are introduced
and their properties are studied and relations between them are given in this paper. It is …