First neighborhood complete ideals in two-dimensional Muhly local domains are projectively full

Author:
Raymond Debremaeker

Journal:
Proc. Amer. Math. Soc. **137** (2009), 1649-1656

MSC (2000):
Primary 13B22, 13H10

Published electronically:
December 10, 2008

MathSciNet review:
2470823

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a two-dimensional Muhly local domain, i.e., an integrally closed Noetherian local domain with algebraically closed residue field and the associated graded ring an integrally closed domain.

Motivated by recent work of Ciuperca, Heinzer, Ratliff and Rush on projectively full ideals, we prove that every complete ideal adjacent to the maximal ideal is projectively full.

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Additional Information

**Raymond Debremaeker**

Affiliation:
Department of Mathematics, Katholieke Universiteit, Leuven, Celestijnenlaan 200B-Box 2400, BE-3001 Leuven, Belgium

Email:
raymond.debremaeker@wis.kuleuven.be

DOI:
https://doi.org/10.1090/S0002-9939-08-09735-9

Keywords:
First neighborhood complete ideal,
Muhly local domain,
projectively equivalent ideals,
projectively full ideal

Received by editor(s):
May 8, 2008

Received by editor(s) in revised form:
August 6, 2008

Published electronically:
December 10, 2008

Communicated by:
Bernd Ulrich

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.