Coprime packedness and set theoretic complete intersections of ideals in polynomial rings
Author:
V. Erdogdu
Journal:
Proc. Amer. Math. Soc. 132 (2004), 3467-3471
MSC (2000):
Primary 13B25, 13B30, 13C15, 13C20; Secondary 13A15, 13A18
DOI:
https://doi.org/10.1090/S0002-9939-04-07438-6
Published electronically:
July 14, 2004
MathSciNet review:
2084066
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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:
https://doi.org/10.1090/S0002-9939-04-07438-6
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