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Matematicheskie Zametki, 2010, Volume 87, Issue 3, Pages 412–416
DOI: https://doi.org/10.4213/mzm4171 (Mi mzm4171) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Abelian Groups as $\mathrm{UA}$-Modules over the Ring $\mathbb Z$

O. V. Ljubimtseva, D. S. Chistyakovb

a Nizhny Novgorod State University of Architecture and Civil Engineering
b N. I. Lobachevski State University of Nizhni Novgorod
Full-text PDF (408 kB) Citations (7)
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DOI: https://doi.org/10.4213/mzm4171
Abstract: Let $V$ be a module over a ring $R$. The module $V$ is called a unique addition module (a $\mathrm{UA}$-module) if there is no new addition on the set $V$ without changing the action of $R$ on $V$. In the paper, the $\mathrm{UA}$-modules over the ring $\mathbb Z$ are found.
Keywords: unitary module over an associative ring, unique addition module, mixed Abelian group, strongly servant subgroup, divisible group, reduced group.
Received: 15.11.2005
Revised: 25.09.2009
English version:
Mathematical Notes, 2010, Volume 87, Issue 3, Pages 380–383
DOI: https://doi.org/10.1134/S0001434610030090
Bibliographic databases:
Document Type: Article
UDC: 512.541
Language: Russian
Citation: O. V. Ljubimtsev, D. S. Chistyakov, “Abelian Groups as $\mathrm{UA}$-Modules over the Ring $\mathbb Z$”, Mat. Zametki, 87:3 (2010), 412–416; Math. Notes, 87:3 (2010), 380–383
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математические заметки Mathematical Notes
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