Coprime packedness and set theoretic complete intersections of ideals in polynomial rings
Author:
V. Erdogdu
Journal:
Proc. Amer. Math. Soc. 132 (2004), 34673471
MSC (2000):
Primary 13B25, 13B30, 13C15, 13C20; Secondary 13A15, 13A18
Published electronically:
July 14, 2004
MathSciNet review:
2084066
Fulltext PDF Free Access
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Abstract: A ring is said to be coprimely packed if whenever is an ideal of and is a set of maximal ideals of with , then for some . Let be a ring and be the localization of at its set of monic polynomials. We prove that if is a Noetherian normal domain, then the ring is coprimely packed if and only if is a Dedekind domain with torsion ideal class group. Moreover, this is also equivalent to the condition that each proper prime ideal of is a set theoretic complete intersection. A similar result is also proved when is either a Noetherian arithmetical ring or a Bézout domain of dimension one.
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Additional Information
V. Erdogdu
Affiliation:
Department of Mathematics, Istanbul Technical University, Maslak, 80626 Istanbul, Turkey
Email:
erdogdu@itu.edu.tr
DOI:
http://dx.doi.org/10.1090/S0002993904074386
PII:
S 00029939(04)074386
Keywords:
Coprime packedness,
polynomial rings,
class group,
set theoretic complete intersection
Received by editor(s):
July 17, 2002
Received by editor(s) in revised form:
June 25, 2003
Published electronically:
July 14, 2004
Communicated by:
Bernd Ulrich
Article copyright:
© Copyright 2004
American Mathematical Society
