Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Incomparable prime ideals in commutative radical Fréchet algebras

Author(s): Hung Le Pham
Journal: Proc. Amer. Math. Soc. 137 (2009), 593-596.
MSC (2000): Primary 46J05; Secondary 46J20, 46J45
Posted: August 22, 2008
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

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.

References:

1.
S. H. Bouloussa, Caractérisation des algèbres de Fréchet qui sont des anneaux de valuation, J. London Math. Soc. (2) 25 (1982), 355-364. MR 653393 (83f:46065)

2.
H. G. Dales, Banach algebras and automatic continuity, London Mathematical Society Monographs, vol. 24, The Clarendon Press, Oxford University Press, New York, 2000. MR 1816726 (2002e:46001)

3.
J. R. Esterle, Theorems of Gel$ ^\prime$fand-Mazur type and continuity of epimorphisms from $ \mathcal{C}(K)$, J. Functional Analysis 36 (1980), 273-286. MR 571409 (81m:46068)

4.
J. R. Esterle, Elements for a classification of commutative radical Banach algebras, in Radical Banach Algebras and Automatic Continuity, Lecture Notes in Mathematics, Vol. 975 (1983), 4-65, Springer, Berlin, Heidelberg, and New York. MR 697578 (84h:46064)

5.
H. L. Pham, The continuity of homomorphisms and derivations from Banach algebras, Ph.D. thesis, University of Leeds, 2005.

6.
B. H. Williams, Combinatorial Set Theory, North-Holland Pub. Co., Amsterdam, New York, 1977.

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46J05, 46J20, 46J45

Retrieve articles in all Journals with MSC (2000): 46J05, 46J20, 46J45

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: 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
Posted: August 22, 2008
Additional Notes: This research is supported by a Killam Postdoctoral Fellowship and an Honorary PIMS PDF
Communicated by: Nigel J. Kalton
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google