Strong exchange rings

• Cortés-Izurdiaga, Manuel ^[1] ; Guil Asensio, Pedro A. ^[2]
  1. [1] Universidad de Málaga

     Universidad de Málaga

     Málaga, España

     
  2. [2] Universidad de Murcia

     Universidad de Murcia

     Murcia, España

     
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 67, Nº 0, 2023, págs. 541-567
• Idioma: inglés
• DOI: 10.5565/publmat6722303
• Enlaces
  • Texto completo
• Resumen

  • 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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