Mohammed [MI371 introduced the following concept. A module P is J-projective, J the
Jacobson radical of B, provided whenever X+ Y is an epimorphism of B-modules with JY= 0 …

The definition of the determinant of an endomorphism of a free module depends on the
following fact: If F is a free R-module of rank n, then the homogeneous component∧ nF, of …

Itiswellknownthattheendomorphismring [)= End (RE) ofa finitely
generatedprojectivemoduleE overa commutativeringR isa separableR ｭ algebrawithR/αits …

In § 1 of this note we first define the trace of an endomorphism of a projective module P over
a non-commutative ring A. Then we call the trace of the identity the rank element r (P) of P …

1. Introduction and preliminaries. A left R-module M is called locally projective [10] if given
an epimorphismf: A-~ B, some 9 6 Hom (M, B) and a finitely generated submodule F of M …

Rosenberg and Zelinsky [6] first addressed the question of characterizing for a ring R those
simple modules RT having injective hulls of finite length. In that work they also announced a …

Commentationes Mathematicae Universitatis Carolinae Page 1 Commentationes Mathematicae
Universitatis Carolinae Pavel Příhoda Add(U) of a uniserial module Commentationes …

1. In this paper, the structure theorems of I~ AGAO and l~ AXAYAMA [4] for projective and
injective modules over certain rings are derived by methods different from those used in [4] …

Throughout R will denote a ring with identity and every Λ-modules considered in this note
are unitary Λ-modules. Let M be an Λ-module. If End^(M) is a local ring, we call M a …