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A Note on the Dubois-Efroymson Dimension Theorem

Published online by Cambridge University Press:  20 November 2018

Wojciech Kucharz
Wojciech Kucharz*
Affiliation:
Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131, USA
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Abstract

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Let X ⊂ Rnn be an irreducible nonsingular algebraic set and let Z be an algebraic subset of X with dim Z ≦ dim X — 2. In this paper it is shown that there exists an irreducible algebraic subset Y of X satisfying the following conditions: dim Y = dim X — 1, Z ⊂ Y and that the ideal of regular functions on X vanishing on Y is principal.

Keywords

14G3014J99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 1 , 01 March 1989 , pp. 24 - 29
Copyright
Copyright © Canadian Mathematical Society 1989

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