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 …

Throughout, R denotes a commutative ring with identity, an R-module means a unitary. R-
module and an Artinian K-module means an/^-module with the descending chain condition …

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 …

Does Hopkins' theorem extend to projective modules, ie, are projective Artinian modules
Noetherian? An example is given to answer this question in the negative; however, we show …

The object of this paper is to investigate finitely generated modules and injective modules
over fully bounded Noetherian rings. Our main results on fg modules (Theorems 3.1 and 3.4) …

If N is a Noetherian module over the commutative ring R (throughout the paper, R will
denote a commutative ring with identity), then the study of N in many contexts can be …

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 …

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 …

P. Vámos introduced in [3] a notion for modules dual to that of “finitely generated”. The
author studied this condition in his thesis, referring to modules which satisfy it as “quasi …

It is well known that if RCS are rings (rings in this paper have units but need not be
commutative) such that S is finitely generated as a left R-module, then S is Noetherian or …