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Matematicheskie Zametki, 2012, Volume 91, Issue 6, Pages 934–941
DOI: https://doi.org/10.4213/mzm4125 (Mi mzm4125) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Abelian Groups as $\mathrm{UA}$-Modules over Their Endomorphism Ring

D. S. Chistyakov

N. I. Lobachevski State University of Nizhni Novgorod
Full-text PDF (421 kB) Citations (6)
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DOI: https://doi.org/10.4213/mzm4125
Abstract: Suppose that $V$ is a module over a ring $R$. The module $V$ is called a unique addition module ($\mathrm{UA}$-module) if it is not possible to change the addition on the set $V$ without changing the action of $R$ on $V$. In this paper, we find Abelian groups that are $\mathrm{UA}$-modules over their endomorphism ring.
Keywords: unique addition module, Abelian group, torsion-free group, quasidecomposition of a group, distributive module, irreducible module, uniserial module, endomorphism ring.
Received: 05.11.2010
Revised: 24.01.2011
English version:
Mathematical Notes, 2012, Volume 91, Issue 6, Pages 878–884
DOI: https://doi.org/10.1134/S0001434612050355
Bibliographic databases:
Document Type: Article
UDC: 512.541
Language: Russian
Citation: D. S. Chistyakov, “Abelian Groups as $\mathrm{UA}$-Modules over Their Endomorphism Ring”, Mat. Zametki, 91:6 (2012), 934–941; Math. Notes, 91:6 (2012), 878–884
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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