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

Debremaeker, Raymond

doi:10.1090/S0002-9939-08-09735-9

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
DOI: https://doi.org/10.1090/S0002-9939-08-09735-9
Published electronically: December 10, 2008
MathSciNet review: 2470823
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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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