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

 

Essential domains and two conjectures in dimension theory


Authors: M. Fontana and S. Kabbaj
Journal: Proc. Amer. Math. Soc. 132 (2004), 2529-2535
MSC (2000): Primary 13C15, 13F20, 13F05, 13G05, 13B02, 13B30
Published electronically: April 21, 2004
MathSciNet review: 2054776
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Abstract: This note investigates two long-standing conjectures on the Krull dimension of integer-valued polynomial rings and of polynomial rings in the context of (locally) essential domains.


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Additional Information

M. Fontana
Affiliation: Dipartimento di Matematica, Università degli Studi “Roma Tre”, Largo San L. Murialdo 1, 00146 Roma, Italy
Email: fontana@mat.uniroma3.it

S. Kabbaj
Affiliation: Department of Mathematics, P.O. Box 5046, KFUPM, Dhahran 31261, Saudi Arabia
Email: kabbaj@kfupm.edu.sa

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07502-1
PII: S 0002-9939(04)07502-1
Keywords: Krull dimension, valuative dimension, Jaffard domain, integer-valued polynomial ring, essential domain, Krull domain, UFD, PVMD, Kronecker function ring, star operation
Received by editor(s): January 15, 2003
Published electronically: April 21, 2004
Additional Notes: The first author was partially supported by a research grant MIUR 2001/2002 (Cofin 2000-MM01192794). The second author was supported by the Arab Fund for Economic and Social Development
This work was done while both authors were visiting Harvard University
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2004 American Mathematical Society