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Mat. Zametki, 2017, Volume 101, Issue 3, Pages 425–429 (Mi mz10878)  

Nonreduced Abelian Groups with $\mathrm{UA}$-Rings of Endomorphisms

O. V. Ljubimtsev

Nizhny Novgorod State University of Architecture and Civil Engineering

Abstract: A ring $K$ is a unique addition ring (a $\mathrm{UA}$-ring) if its multiplicative semigroup $(K, \cdot )$ can be equipped with a unique binary operation $+$ transforming this semigroup to a ring $(K, \cdot ,+)$. An Abelian group is called an $\operatorname{End}$-$\mathrm{UA}$-group if its endomorphism ring is a $\mathrm{UA}$-ring. In the paper, we find $\operatorname{End}$-$\mathrm{UA}$-groups in the class of nonreduced Abelian groups.

Keywords: Abelian group, endomorphism ring.

DOI: https://doi.org/10.4213/mzm10878

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English version:
Mathematical Notes, 2017, 101:3, 484–487

Bibliographic databases:

UDC: 512.541
Received: 20.05.2016

Citation: O. V. Ljubimtsev, “Nonreduced Abelian Groups with $\mathrm{UA}$-Rings of Endomorphisms”, Mat. Zametki, 101:3 (2017), 425–429; Math. Notes, 101:3 (2017), 484–487

Citation in format AMSBIB
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