First neighborhood complete ideals in twodimensional Muhly local domains are projectively full
Author:
Raymond Debremaeker
Journal:
Proc. Amer. Math. Soc. 137 (2009), 16491656
MSC (2000):
Primary 13B22, 13H10
Published electronically:
December 10, 2008
MathSciNet review:
2470823
Fulltext PDF
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Abstract: Let be a twodimensional 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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 S.D. Cutkosky, On unique and almost unique factorization of complete ideals. II, Invent. Math. 98 (1) (1989) 5974. MR 1010155 (90j:14016b)
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 J. FernándezSánchez, Factorization of complete ideals in normal birational extensions in dimension two, J. Algebra 314 (2007) 344361. MR 2331766
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 C. Huneke, J.D. Sally, Birational extensions in dimension two and integrally closed ideals, J. Algebra 115 (2) (1988) 481500. MR 943272 (89e:13025)
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Additional Information
Raymond Debremaeker
Affiliation:
Department of Mathematics, Katholieke Universiteit, Leuven, Celestijnenlaan 200BBox 2400, BE3001 Leuven, Belgium
Email:
raymond.debremaeker@wis.kuleuven.be
DOI:
http://dx.doi.org/10.1090/S0002993908097359
PII:
S 00029939(08)097359
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.
