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WINTER 2013 Muhly local domains and Zariski's theory of complete ideals
Raymond Debremaeker
J. Commut. Algebra 5(4): 507-526 (WINTER 2013). DOI: 10.1216/JCA-2013-5-4-507

Abstract

Let $(R,\M)$ be a two-dimensional Muhly local domain, that is, a two-dimensional integrally closed Noetherian local domain with algebraically closed residue field and with the associated graded ring $\text{gr}_{\M}R$ an integrally closed domain. In this paper we show that a number of fundamental results of Zariski's theory of complete ideals in two-dimensional regular local rings are not necessarily valid in $R$. However, if the associated graded ring $\text{gr}_{\M}R$ satisfies an additional assumption as in work of Muhly and Sakuma, then we are able to show that ``any product of contracted ideals is contracted'' holds in $R$ if and only if $R$ has minimal multiplicity.

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Raymond Debremaeker. "Muhly local domains and Zariski's theory of complete ideals." J. Commut. Algebra 5 (4) 507 - 526, WINTER 2013. https://doi.org/10.1216/JCA-2013-5-4-507

Information

Published: WINTER 2013
First available in Project Euclid: 31 January 2014

zbMATH: 1376.13004
MathSciNet: MR3161744
Digital Object Identifier: 10.1216/JCA-2013-5-4-507

Subjects:
Primary: 13B22 , 13H10

Keywords: complete ideal , contracted ideal , Muhly local domain , regular local ring

Rights: Copyright © 2013 Rocky Mountain Mathematics Consortium

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Vol.5 • No. 4 • WINTER 2013
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