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

Juan Carlos Cabello Piñar , Miguel Cabrera García , Eduardo Antonio Nieto Arco

• 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.