We identify a large class of rings over which locally free modules are determined by their
endomorphism rings. We characterize these endomorphism rings and consider under what …

This is a study of the conditions under which smallness of proper submodules will influence
the structure of the endomorphism ring of a module. The case in which that endomorphism …

We derive a necessary and sufficient condition that an isomorphism between the
endomorphism rings of modules be induced by a semi-linear isomorphism of the modules …

The paper is a study of modules with a local endomorphism ring. We consider
decompositions of modules and give a simple proof of Azumaya's theorem. We also define …

We consider the question of how minimal acyclic complexes of finitely generated free
modules arise over a commutative local ring. A standard construction gives that every totally …

We will realize certain topological rings as endomorphism rings of] 1-free abelian groups of
cardinality] 1 where the isomorphism is also a homeomorphism relating the topology on the …

A module RM is said to be retractable if HomR (M, U)≠ 0 for each nonzero submodule U of
M. M is said to be a CS module if every complement submodule of M is a direct summand in …

ABSTRACT A module M Is said to be weakly projective If and only If It has a projective cover
11": P (M)--+ M and every map from P (M) Into a finitely generated (free) module can be …

A module M is said to be weakly N-projective if it has a projective cover π: P (M)↠ M and for
each homomorphism: P (M)→ N there exists an epimorphism σ: P (M)↠ M such that (kerσ) …

On rings with one middle class of injectivity domains 1. Introduction Page 1 MATHEMATICAL
COMMUNICATIONS 109 Math. Commun. 27(2022), 109–126 On rings with one middle class …