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

 

Incomparable prime ideals in commutative radical Fréchet algebras


Author: Hung Le Pham
Journal: Proc. Amer. Math. Soc. 137 (2009), 593-596
MSC (2000): Primary 46J05; Secondary 46J20, 46J45
Published electronically: August 22, 2008
MathSciNet review: 2448580
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Abstract: Let $ R$ be a commutative radical Fréchet algebra having a non-nilpotent element $ a$ with $ a\in \overline{Ra}$. Then $ R$ contains a continuum of incomparable prime ideals.


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Additional Information

Hung Le Pham
Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
Email: hlpham@math.ualberta.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09665-2
PII: S 0002-9939(08)09665-2
Keywords: Commutative Fr\'{e}chet algebra, radical, Banach algebra, prime ideal
Received by editor(s): January 23, 2008
Published electronically: August 22, 2008
Additional Notes: This research is supported by a Killam Postdoctoral Fellowship and an Honorary PIMS PDF
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.