This volume provides a comprehensive introduction to module theory and the related part of
ring theory, including original results as well as the most recent work. It is a useful and …

Let Cc (X) ff PC (X): f (X) is countableg. Similar to C (X) it is observed that the sum of any
collection of semiprime (resp. prime) ideals in the ring Cc (X) is either Cc (X) or a semiprime …

Modules in which every proper submodule (resp. proper nonzero submodule) is prime
(called fully prime (almost fully prime)) and with some other related notions are fully …

Let CF (X) denote the socle of C (X). It is shown that X is a P-space if and only if C (X) is a ℵ0-
selfinjective ring or equivalently, if and only if is ℵ0-selfinjective. We also prove that X is an …

In this article we introduce the concept of $ r $-ideals in commutative rings (note: an ideal $ I
$ of a ring $ R $ is called $ r $-ideal, if $ ab\in I $ and ${\rm Ann}(a)=(0) $ imply that $ b\in I …

In answer to a question by L. Fuchs, TS Shores in [26] has shown that if M is a Loewy
module over a commutative ring and IS,) is the ascending Loewy series of M such that S1 …

Introduction. Recently in [6], Theorem 4, it has been shown that if R is a self-~ njective
strongly regular rrng, then the power series ring R [[x]] is a duo ring (ie, every one-sided …

Let R be a commutative ring with identity and R [[x]] be the ring of formal power series with
coefficients in R. In this article we consider sufficient conditions in order that P [[x]] is a …

An R-module M is called strongly duo if Tr (N, M)= N for every N≤ MR. Several equivalent
conditions to being strongly duo are given. If MR is strongly duo and reduced, then End R …

In this note we investigate ℵ0-injectivity of rings and modules and review the literature
around this topic. We observe that several characterizations of rings by injectivity can be …