Let be an ideal of Noetherian ring R and let s be a non-negative integer. Let M be an R-
module such that is finite R-module. If s is the first integer such that the local cohomology …

It is proved that if R is a right FBN ring then a non-zero right R-module M has the property
that HomR (M, N)≠ 0 for every non-zero submodule N of M if and only if HomR (M, R/P)≠ 0 …

Our aim in this note is to generalize some topological results of commutative noetherian
rings to non-commutative rings. As a supplemental remark of [2] we prove in § 1 that any …

In many important theorems in the homological theory of commutative local rings, an
essential ingredient in the proof is to consider We examine these annihilators for an arbitrary …

Kaplansky proved in [3, Theorem 2] that over a local 1 ring any projective module is free.
Another large class of projective modules were shown to be free a few years later. Bass [2 …

Advances in Algebra and Model Theory Page 1 A construction of endofinite modules Claus
Michael Ringel Fakultat fur Mathematik, Universitat Bielefeld D-33501 Bielefeld, Germany …

We prove that the Krull-Schmidt theorem fails for artinian modules. This answers a question
asked by Krull in 1932. In fact we show that if S is a module-finite algebra over a semilocal …

In this paper we exhibit certain modules $ A $ over a commutative noetherian local ring
$(R,\mathfrak {M}) $ which test projective dimension of finitely generated modules in the …

A well-known result of 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 and only if R is an Artinian …

Let (R, m) be a Noetherian local ring and I an ideal of R. Let M be a finitely generated R-
module with dimM= d. It is clear by Matlis duality that if R is complete then HId (M) satisfies …