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Algebraically Compact Abelian Groups with UA-Rings of Endomorphisms

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Abstract

A ring K is said to be a unique addition ring (UA-ring) if on its multiplicative semigroup (K, ·) it is possible to set only one binary operation of + turning (K, ·, +) into a ring. We call an Abelian group an End-UA-group if its endomorphism ring is a UA-ring. In this paper, End-UA-groups are found in a class of algebraically compact Abelian groups.

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Authors and Affiliations

  1. Nizhny Novgorod State Architectural and Construction University, Ilyinskaya St., 65, Nizhny Novgorod, 603109, Russia

    O. V. Lyubimtsev

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  1. O. V. Lyubimtsev
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Correspondence to O. V. Lyubimtsev.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 20, No. 5, pp. 121–129, 2015.

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Lyubimtsev, O.V. Algebraically Compact Abelian Groups with UA-Rings of Endomorphisms. J Math Sci 230, 433–438 (2018). https://doi.org/10.1007/s10958-018-3750-z

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  • DOI: https://doi.org/10.1007/s10958-018-3750-z

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