Let $ R $ be a commutative ring with identity, let $ X $ be an indeterminate, and let $ I $ be
an ideal of the polynomial ring $ R [X] $. Let $\min I $ denote the set of elements of $ I $ of …

Let $ R $ be a commutative Noetherian ring, $\fa $ an ideal of $ R $, $ M $ an arbitrary $ R $-
module and $ N $ a finite $ R $-module. We prove that\cite [Theorem 2.1]{Mel} and\cite …

Let R be a commutative ring with 1 and A a module finite R-algebra. Let Mod A denote the
category of finitely generated A-modules. If R'is a commutative extension of R, one can form …

τ-INJECTIVE SUBMODULES OF INDECOMPOSABLE INJECTIVE MODULES Septimiu Crivei 1.
Introduction and preliminaries The problem of det Page 1 J. Korean Math. Soc. 43 (2006), No. 1 …

We study direct-sum decompositions of RD-projective modules. In particular, we investigate
the rings over which every RD-projective right module is a direct sum of cyclically presented …

This paper continues the study of an R-module M through properties of the category a [M] of
submodules of M-generated modules. It is shown that a self-projective M is locally artinian if …

A theorem from commutative algebra due to Köthe and Cohen-Kaplansky states that,“a
commutative ring R has the property that every R-module is a direct sum of cyclic modules if …

Rings whose finitely generated modules are extending Page 1 JOURNAL OF PURE AND
Journal of Pure and Applied Algebra 111 (1996) 325-328 APPLIED ALGEBRA Rings whose …

Let $ R $ be a commutative semilocal noetherian ring, $\Lambda $ a left noetherian $ R $-
algebra and $ M, N $ finitely generated left $\Lambda $-modules such that ${\operatorname …

In this work we continue studying the notion of completion of R-modules, over a commutative
ring R, relative to a torsion theory ϑ. We develop some techniques relative to localization at …