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Algebra Discrete Math., 2009, Issue 3, Pages 85–93 (Mi adm137)  

This article is cited in 5 scientific papers (total in 5 papers)

RESEARCH ARTICLE

A note on a problem due to Zelmanowitz

V. S. Rodriguesa, A. A. Santanab

a 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.

Full text: PDF file (211 kB)

Bibliographic databases:
MSC: 16D10, 16D80, 16D99
Received: 20.08.2009
Revised: 24.09.2009
Language:

Citation: V. S. Rodrigues, A. A. Santana, “A note on a problem due to Zelmanowitz”, Algebra Discrete Math., 2009, no. 3, 85–93

Citation in format AMSBIB
\Bibitem{RodSan09}
\by V.~S.~Rodrigues, A.~A.~Santana
\paper A note on a~problem due to Zelmanowitz
\jour Algebra Discrete Math.
\yr 2009
\issue 3
\pages 85--93
\mathnet{http://mi.mathnet.ru/adm137}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2640391}
\zmath{https://zbmath.org/?q=an:1199.16017}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Borges I., Lomp Ch., “Irreducible Actions and Compressible Modules”, J. Algebra. Appl., 10:1 (2011), 101–117  crossref  mathscinet  zmath  isi  scopus
    2. Dutta H., Hoque A., Saeed S.M., “Some Aspects of Quasi-Pseudo Principally Injective Modules”, J. Ramanujan Math. Soc., 31:3 (2016), 257–263  mathscinet  isi
    3. Singh A.K., Mahato A.K., Shum K.P., “Quasi-Coretractable Modules”, Asian-Eur. J. Math., 10:3 (2017), 1750042  crossref  mathscinet  zmath  isi  scopus
    4. Diallo A.D., Diop P.Ch., Barry M., “On E-Small Monoform Modules”, JP J. Algebr. Number Theory Appl., 40:3 (2018), 305–320  crossref  isi
    5. Singh A.K., Mahato A.K., “Critically Compressible Modules”, Southeast Asian Bull. Math., 42:1 (2018), 131–140  mathscinet  zmath  isi
  • Algebra and Discrete Mathematics
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