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Essential domains and two conjectures in dimension theory
Author(s):
M.
Fontana;
S.
Kabbaj
Journal:
Proc. Amer. Math. Soc.
132
(2004),
2529-2535.
MSC (2000):
Primary 13C15, 13F20, 13F05, 13G05, 13B02, 13B30
Posted:
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.
References:
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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:
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
Posted:
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
Copyright of article:
Copyright
2004,
American Mathematical Society
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