Closed Prime Ideals in Algebras with Semiprime Multiplication Algebra |
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Authors: | J. C. Cabello M. Cabrera E. Nieto |
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Affiliation: | 1. Department of Mathematical Analysis, Faculty of Science , University of Granada , Granada, Spain jcabello@ugr.es;3. Department of Mathematical Analysis, Faculty of Science , University of Granada , Granada, Spain |
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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 ?. In fact, these sets agree for both closures. The same can be said in M(A) for the closure operations π and ?′. 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. |
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Keywords: | Closure operations Multiplication algebra Prime ideals Semiprime algebras |
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