IYTRODCCTION 1: n~ onorphism rings of various types of modules have been objects of
extensive study in the recent past [2, 11, 14, 15, 18, 25, 261. In [15] Erika Mares introduced …

(Sketch). is done. If R has stable range 1 then, by a theorem of Kaplansky [16, 4.7], the same
is true for the endomorphism ring of any finitely generated projective R-module. So R unit …

The following conditions are shown to be equivalent: 1) ring A is generalized uniserial (not
necessarily artinian); 2) every finitely presented A module is semiserial; 3) A is semiperfect …

On Finitely Generated Modules Over Noetherian Rings Page 1 ON FINITELY GENERATED
MODULES OVER NOETHERIAN RINGS BY JP JANS(Q) 0. Introduction. If A is a module over a …

A module is said to be extending, if every closed (ie complement) submodule is a direct
summand. This property is usually denoted by (Q). It is, obviously, equivalent to the …

The (unital right) module M (over the ring R with identity) is said to have the summand
intersection property if the intersection of any two direct summands of M is a direct …

M commutes. The first section of this paper contains results which are needed to prove a
decomposition theorem for quasi-projective modules over left perfect rings (Theorem 1.10) …

Some theorems in [4] indicate that the injective modules over a ring R provide a great deal of
information about the structure of the ring. More recently, the papers of H. Bass [9] and C …

Let $ R $ be an algebra over a field $ k $, and $ P, Q $ be two nonzero finitely generated
projective $ R $-modules. By adjoining further generators and relations to $ R $, one can …

In § 1, we begin with a basic theorem which describes a convenient embedding of a
nonsingular left R-module into a complete direct product of copies of the left injective hull of …