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

  1. Cabello Piñar, Juan Carlos
  2. Cabrera García, Miguel
  3. Nieto Arco, Eduardo Antonio
Revista:
Extracta mathematicae

ISSN: 0213-8743

Año de publicación: 2012

Volumen: 27

Número: 2

Páginas: 231-244

Tipo: Artículo

Otras publicaciones en: Extracta mathematicae

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.