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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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Let $(R, \mathcal {M})$ 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 $\mathcal {M}$ 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

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.