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Title: Algebraically Compact Abelian Groups with UA-Rings of Endomorphisms

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.

Authors:
 [1]
  1. Nizhny Novgorod State Architectural and Construction University (Russian Federation)
Publication Date:
OSTI Identifier:
22771350
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Sciences
Additional Journal Information:
Journal Volume: 230; Journal Issue: 3; Conference: 5. All-Russian symposium on abelian groups, Biysk (Russian Federation), 20-25 Aug 2012; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ALGEBRA; GROUP THEORY; RINGS; TOPOLOGICAL MAPPING

Citation Formats

Lyubimtsev, O. V., E-mail: Oleg-lyubimcev@mail.ru. Algebraically Compact Abelian Groups with UA-Rings of Endomorphisms. United States: N. p., 2018. Web. doi:10.1007/S10958-018-3750-Z.
Lyubimtsev, O. V., E-mail: Oleg-lyubimcev@mail.ru. Algebraically Compact Abelian Groups with UA-Rings of Endomorphisms. United States. doi:10.1007/S10958-018-3750-Z.
Lyubimtsev, O. V., E-mail: Oleg-lyubimcev@mail.ru. Sun . "Algebraically Compact Abelian Groups with UA-Rings of Endomorphisms". United States. doi:10.1007/S10958-018-3750-Z.
@article{osti_22771350,
title = {Algebraically Compact Abelian Groups with UA-Rings of Endomorphisms},
author = {Lyubimtsev, O. V., E-mail: Oleg-lyubimcev@mail.ru},
abstractNote = {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.},
doi = {10.1007/S10958-018-3750-Z},
journal = {Journal of Mathematical Sciences},
issn = {1072-3374},
number = 3,
volume = 230,
place = {United States},
year = {2018},
month = {4}
}