Abstract
Let A be an algebra whose multiplication algebra M(A) is semiprime. We prove that, except in an exceptional case, the proper closed prime ideals of A are the maximal closed ideals of A, for the closure operations π and ϵ. In fact, these sets agree for both closures. The same can be said in M(A) for the closure operations π and ϵ′. Moreover, we establish the relationships between the proper closed prime ideals of A and the ones of the algebras M(A),U and A/U, for a given ideal U of A.
2000 Mathematics Subject Classification:
ACKNOWLEDGMENTS
This research was partially supported by the Spanish MEC Project MTM2005-02159 and the Junta de Andalucía Grant FQM290.
Notes
Communicated by M. Ferrero.