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

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**137**(2009), 1649-1656 Request permission

## Abstract:

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
- Email: raymond.debremaeker@wis.kuleuven.be
- 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
- © Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**137**(2009), 1649-1656 - MSC (2000): Primary 13B22, 13H10
- DOI: https://doi.org/10.1090/S0002-9939-08-09735-9
- MathSciNet review: 2470823