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Some remarks on biequidimensionality of topological spaces and Noetherian schemes
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2017 (English)In: Journal of Commutative Algebra, ISSN 1939-0807, E-ISSN 1939-2346, Vol. 9, no 1, 49-63 p.Article in journal (Refereed) Published
Abstract [en]

There are many examples of the fact that dimension and codimension behave somewhat counterintu- itively. In [2], 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.

Place, publisher, year, edition, pages
Rocky Mountain Mathematics Consortium , 2017. Vol. 9, no 1, 49-63 p.
Keyword [en]
Biequidimensionality, Codimension function, Dimension formula, Spectrum of a Noetherian ring
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-207386DOI: 10.1216/JCA-2017-9-1-49ScopusID: 2-s2.0-85017394917OAI: oai:DiVA.org:kth-207386DiVA: diva2:1107493
Note

QC 20170609

Available from: 2017-06-09 Created: 2017-06-09 Last updated: 2017-06-09Bibliographically approved

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