This article is cited in 5 papers

RESEARCH ARTICLE

A note on a problem due to Zelmanowitz

V. S. Rodrigues^a, A. A. Santana<sup>b

a</sup> Departamento de Matemática Universidade Federal de Santa Catarina 88040–900 – Florianópolis – Brazil
^b Instituto de Matemática Universidade Federal do Rio Grande do Sul 91509–900 –Porto Alegre – Brazil

Abstract: In this paper we consider a problem due to Zelmanowitz. Specifically, we study under what conditions a uniform compressible module whose nonzero endomorphisms are monomorphisms is critically compressible. We give a positive answer to this problem for the class of nonsingular modules, quasi-projective modules and for modules over rings which are in a certain class of rings which contains at least the commutative rings and the left duo rings.

Keywords: Compressible; critically compressible; uniform; polyform; left duo ring.

MSC: 16D10, 16D80, 16D99

Received: 20.08.2009
Revised: 24.09.2009

Language: English

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