Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 47, No. 1, pp. 121-135 (2006)

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The effect of quadratic transformations on degree functions

R. Debremaeker and V. Van Lierde

Monitoraat Wiskunde, K.U.Leuven, Celestijnenlaan 200C, 3001 Heverlee, Belgium, e-mail:; Al Akhawayn University, P.O. Box 1828 Avenue Hassan II, Ifrane 53000, Morocco

Abstract: We study the effect of a quadratic transformation on the degree function of a $0$-dimensional ideal with only one Rees valuation in a $2$-dimensional regular local ring with algebraically closed residue field. A number of important results of Zariski and Lipman about complete ideals in a $2$-dimensional regular local ring follow as quick corollaries. Necessary and sufficient conditions for the regularity of a $2$-dimensional normal local domain are proved.

Keywords: degree function, quadratic transformation, regular local ring, complete ideals

Classification (MSC2000): 13H05, 13H15

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Electronic version published on: 9 May 2006. This page was last modified: 4 Nov 2009.

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