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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The strong radical and finite-dimensional ideals


Author: Bertram Yood
Journal: Proc. Amer. Math. Soc. 130 (2002), 139-143
MSC (2000): Primary 46H10; Secondary 16D25
Published electronically: May 23, 2001
MathSciNet review: 1855630
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Abstract: Let $A$ be a semi-prime Banach algebra with strong radical ${\mathfrak R}$ (intersection of its two-sided modular maximal ideals). A minimal left or right ideal $K$ of $A$ is infinite-dimensional if and only if $K \subset {\mathfrak R}$. Thus all minimal one-sided ideals in $A$ are finite-dimensional if $A$ is strongly semi-simple.


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Additional Information

Bertram Yood
Affiliation: Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06049-X
PII: S 0002-9939(01)06049-X
Received by editor(s): January 7, 2000
Received by editor(s) in revised form: June 10, 2000
Published electronically: May 23, 2001
Communicated by: Dale Alspach
Article copyright: © Copyright 2001 American Mathematical Society