Strong exchange rings
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 sho...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:280956 |
| Acceso en línea: | https://ddd.uab.cat/record/280956 https://dx.doi.org/urn:doi:10.5565/PUBLMAT6722303 |
| Access Level: | acceso abierto |
| Palabra clave: | Exchange rings Von neumann regular rings Semiregular rings (pure-)injective rings Coprime pair |
| Sumario: | 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. |
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