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

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

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Title: Semicentral idempotents in the multiplication ring of a centrally closed prime ring
Author: Cabello, J.C.; Cabrera, M.; Nieto, E.
Abstract: Let R be a ring and let M(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.
URI: http://hdl.handle.net/10662/10358
Date: 2012


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