Semicentral idempotents in the multiplication ring of a centrally closed prime ring

• Autores: Juan Carlos Cabello Piñar, Miguel Cabrera García, Eduardo Antonio Nieto Arco
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 27, Nº 2, 2012, págs. 231-244
• Idioma: inglés
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• Resumen

  • Let R be a ring and letM(R) stand for the multiplication ring of R. An idempotent E in M(R) is called left semicentral if its range E(R) is a right ideal of R. In the case that R is prime and centrally closed we give a description of the left semicentral idempotents in M(R). As an application we prove that, if, in addition, M(R) is Baer (respectively, regular or Rickart), then R is Baer (respectively, regular or Rickart). Similar results for -rings are also proved.