Strong exchange rings
Cortes-Izurdiaga, Manuel (Universidad de Málaga. Departamento de Matemática Aplicada)
Guil Asensio, Pedro A. (Universidad de Murcia. Departamento de Matemáticas)

Date:	2023
Abstract:	Two elements a, b in a ring R form a right coprime pair, written ha, bi, if aR + bR = R. Right coprime pairs have shown to be quite useful in the study of left cotorsion or exchange rings. In this paper, we define the class of right strong exchange rings in terms of descending chains of them. We show that they are semiregular and that this class of rings contains left injective, left pure-injective, left cotorsion, local, and left continuous rings. This allows us to give a unified study of all these classes of rings in terms of the behaviour of descending chains of right coprime pairs.
Grants:	Agencia Estatal de Investigación PID2020-113552GB-I00 Agencia Estatal de Investigación PID2020-113206GB-I00
Note:	Altres ajuts: The first author is partially supported by the Spanish Government under grants PID2020-113552GB-I00, which include EU FEDER funds, and by the Junta de Andalucía under grant P20-00770. The second author is partially supported by the Spanish Government under grant PID2020-113206GB-I00/AEI/10.13039/501100011033, which includes EU FEDER funds, and by Fundación Séneca of Murcia under grant 19880/GERM/15.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Exchange rings ; Von neumann regular rings ; Semiregular rings ; (pure-)injective rings ; Coprime pair
Published in:	Publicacions matemàtiques, Vol. 67 Núm. 2 (2023) , p. 541-567 (Articles) , ISSN 2014-4350

Adreça original: https://raco.cat/index.php/PublicacionsMatematiques/article/view/418408
DOI: 10.5565/PUBLMAT6722303

27 p, 372.3 KB

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