On fusible rings

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Date
2023-03-20
Authors
Gümüşel, Günseli
Koşan, M. Tamer
Žemlička, Jan
Journal Title
Journal ISSN
Volume Title
Publisher
Communications in Algebra
Abstract
A ring R is called left fusible if every nonzero element is the sum of a left zero-divisor and a non-left zero-divisor, and R is called uniquely left fusible if for any a∈R there exists a unique left zero-divisor z such that a – z is non-left zero-divisor. We show that a left fusible ring R is uniquely left fusible if and only if either R is a domain or R has a unique non-left zero-divisor element.
Description
Published by Communications in Algebra; https://doi.org/10.1080/00927872.2023.2187642; Günseli Gümüşel, Atilim University, Ankara, Turkey; M. Tamer Koşan, Department of Mathematics, Faculty of Sciences, Gazi University, Ankara, Turkey; Jan Žemlicka, Department of Algebra, Faculty of Mathematics and Physics, Charles University, Praha 8, Czechia.
Keywords
Fusible ring; regular element;unit; zero-divisor 2020 MATHEMATICS SUBJECT CLASSIFICATION Primary: 16D40; 16D50; 16D60; 16S34
Citation
http://hdl.handle.net/20.500.14411/1993