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2017 Some remarks on biequidimensionality of topological spaces and Noetherian schemes
Katharina Heinrich
J. Commut. Algebra 9(1): 49-63 (2017). DOI: 10.1216/JCA-2017-9-1-49

Abstract

There are many examples of the fact that dimension and codimension behave somewhat counterintuitively. In \cite {EGAIV1}, it is stated that a topological space is equidimensional, equicodimensional and catenary if and only if every maximal chain of irreducible closed subsets has the same length. We construct examples that show that this is not even true for the spectrum of a Noetherian ring. This gives rise to two notions of biequidimensionality, and we show how these relate to the dimension formula and the existence of a codimension function.

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Katharina Heinrich. "Some remarks on biequidimensionality of topological spaces and Noetherian schemes." J. Commut. Algebra 9 (1) 49 - 63, 2017. https://doi.org/10.1216/JCA-2017-9-1-49

Information

Published: 2017
First available in Project Euclid: 5 April 2017

zbMATH: 1365.13018
MathSciNet: MR3631826
Digital Object Identifier: 10.1216/JCA-2017-9-1-49

Subjects:
Primary: 13C15 , 13E05 , 14A05 , 14A25

Keywords: Biequidimensionality , codimension function , dimension formula , spectrum of a Noetherian ring

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.9 • No. 1 • 2017
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