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

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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