Some remarks on biequidimensionality of topological spaces and Noetherian schemes
(English)Manuscript (preprint) (Other academic)
There are many examples of the fact that dimension and codimension behave somewhat counterintuitively. In EGA 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.
Algebra and Logic
Research subject Mathematics
IdentifiersURN: urn:nbn:se:kth:diva-143965OAI: oai:DiVA.org:kth-143965DiVA: diva2:709963
QS 20142014-04-032014-04-032014-04-04Bibliographically approved