2023 STRONG EXCHANGE RINGS
Manuel Cortés-Izurdiaga, Pedro A. Guil Asensio
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Publ. Mat. 67(2): 541-567 (2023). DOI: 10.5565/PUBLMAT6722303

Abstract

Two elements a, b in a ring R form a right coprime pair, written a,b, 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.

Acknowledgements

The authors would like to thank Professor Pere Ara for several helpful comments and remarks. They also want to thank the referees for several comments and suggestions that improved the quality of this paper.

Citation

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Manuel Cortés-Izurdiaga. Pedro A. Guil Asensio. "STRONG EXCHANGE RINGS." Publ. Mat. 67 (2) 541 - 567, 2023. https://doi.org/10.5565/PUBLMAT6722303

Information

Received: 22 February 2021; Revised: 10 January 2022; Published: 2023
First available in Project Euclid: 29 June 2023

MathSciNet: MR4609011
Digital Object Identifier: 10.5565/PUBLMAT6722303

Subjects:
Primary: 16E50 , 16U40

Keywords: (pure-)injective rings , coprime pair , exchange rings , semiregular rings , von Neumann regular rings

Rights: Copyright © 2023 Universitat Autònoma de Barcelona, Departament de Matemàtiques

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Vol.67 • No. 2 • 2023
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