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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 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 (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 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 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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  • https://doi.org/10.4213/mzm4125
  • https://www.mathnet.ru/eng/mzm/v91/i6/p934
    • This publication is cited in the following 6 articles:
    1. D. S. Chistyakov, “Odnorodnye otobrazheniya smeshannykh modulei”, Chebyshevskii sb., 18:2 (2017), 256–266  mathnet  crossref  elib
    2. D. S. Chistyakov, “On the $\mathrm{UA}$-properties of Abelian $sp$-groups and their endomorphism rings”, J. Math. Sci., 233:5 (2018), 749–754  mathnet  crossref
    3. D. S. Chistyakov, “Separable torsion-free modules with $UA$-rings of endomorphisms”, Russian Math. (Iz. VUZ), 59:6 (2015), 43–48  mathnet  crossref
    4. D. S. Chistyakov, “On homogeneous mappings of finitely presented modules over the ring of polyadic numbers”, J. Math. Sci., 233:1 (2018), 152–156  mathnet  crossref
    5. D. S. Chistyakov, “Homogeneous mappings of Abelian groups”, Russian Math. (Iz. VUZ), 58:2 (2014), 51–57  mathnet  crossref
    6. D. S. Chistyakov, “Abelevy gruppy s UA-koltsom endomorfizmov i ikh odnorodnye otobrazheniya”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2014, no. 4(30), 49–56  mathnet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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