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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
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
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
Linking options:
https://www.mathnet.ru/eng/mzm4171https://doi.org/10.4213/mzm4171 https://www.mathnet.ru/eng/mzm/v87/i3/p412
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Abstract page: | 539 | Full-text PDF : | 184 | References: | 89 | First page: | 4 |
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