Generalizing unit-regular rings and special clean elements

Abstract As a strengthening of the definition of weakly clean rings, given by Šter in J. Algebra (2014), and as a common generalization of the classical unit-regular rings, we define and investigate the class of socalled weakly unit-regular rings as those rings R for which, for every elemen...

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Autor principal:	Danchev,Peter V.
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2020
Materias:	Unit-regular rings Clean rings Special clean elements Weakly clean rings Weakly unit-regular rings
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000501123
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spelling	oai:scielo:S0716-091720200005011232020-11-16Generalizing unit-regular rings and special clean elementsDanchev,Peter V. Unit-regular rings Clean rings Special clean elements Weakly clean rings Weakly unit-regular rings Abstract As a strengthening of the definition of weakly clean rings, given by Šter in J. Algebra (2014), and as a common generalization of the classical unit-regular rings, we define and investigate the class of socalled weakly unit-regular rings as those rings R for which, for every element a ∈ R, there exist a unit u and an idempotent e such that a − u − e ∈ (1 − e)Ra with aR ∩ eR = {0}. Some more exotic relationships with the well-known classes of clean, nil-clean and (strongly) π-regular rings are demonstrated as well. In particular, an elementwise extension of the so-called ”special clean elements” by Khurana et al. in J. Algebra & Appl. (2020) is also processed.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.39 n.5 20202020-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000501123en10.22199/issn.0717-6279-2020-05-0069
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Unit-regular rings Clean rings Special clean elements Weakly clean rings Weakly unit-regular rings
spellingShingle	Unit-regular rings Clean rings Special clean elements Weakly clean rings Weakly unit-regular rings Danchev,Peter V. Generalizing unit-regular rings and special clean elements
description	Abstract As a strengthening of the definition of weakly clean rings, given by Šter in J. Algebra (2014), and as a common generalization of the classical unit-regular rings, we define and investigate the class of socalled weakly unit-regular rings as those rings R for which, for every element a ∈ R, there exist a unit u and an idempotent e such that a − u − e ∈ (1 − e)Ra with aR ∩ eR = {0}. Some more exotic relationships with the well-known classes of clean, nil-clean and (strongly) π-regular rings are demonstrated as well. In particular, an elementwise extension of the so-called ”special clean elements” by Khurana et al. in J. Algebra & Appl. (2020) is also processed.
author	Danchev,Peter V.
author_facet	Danchev,Peter V.
author_sort	Danchev,Peter V.
title	Generalizing unit-regular rings and special clean elements
title_short	Generalizing unit-regular rings and special clean elements
title_full	Generalizing unit-regular rings and special clean elements
title_fullStr	Generalizing unit-regular rings and special clean elements
title_full_unstemmed	Generalizing unit-regular rings and special clean elements
title_sort	generalizing unit-regular rings and special clean elements
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2020
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000501123
work_keys_str_mv	AT danchevpeterv generalizingunitregularringsandspecialcleanelements
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Generalizing unit-regular rings and special clean elements

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