Strong exchange rings

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Manuel Cortes-Izurdiaga
Universidad de Málaga. Departamento de Matemática Aplicada
https://orcid.org/0000-0002-8291-7917
Pedro A. Guil Asensio
Universidad de Murcia. Departamento de Matemáticas
https://orcid.org/0000-0002-0154-9420

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.

Paraules clau
exchange rings, von Neumann regular rings, semiregular rings, (pure-)injective rings, coprime pair

Article Details

Com citar
Cortes-Izurdiaga, Manuel; Guil Asensio, Pedro A. «Strong exchange rings». Publicacions Matemàtiques, 2023, vol.VOL 67, núm. 2, p. 541-67, https://raco.cat/index.php/PublicacionsMatematiques/article/view/418408.
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