Closed Prime Ideals in Algebras with Semiprime Multiplication Algebra |
| |
| Authors: | J C Cabello M Cabrera E Nieto |
| |
| Institution: | 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 |
| |
| 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. |
| |
| Keywords: | Closure operations Multiplication algebra Prime ideals Semiprime algebras |
|
|
