Title

Noether Normalizations, Reductions Of Ideals, And Matroids

Abstract

We show that given a finitely generated standard graded algebra of dimension d over an infinite field, its graded Noether normalizations obey a certain kind of 'generic exchange', allowing one to pass between any two of them in at most d steps. We prove analogous generic exchange theorems for minimal reductions of an ideal, minimal complete reductions of a set of ideals, and minimal complete reductions of multigraded k-algebras. Finally, we unify all these results into a common axiomatic framework by introducing a new topological-combinatorial structure we call a generic matroid, which is a common generalization of a topological space and a matroid. © 2010 American Mathematical Society.

Publication Date

5-13-2011

Publication Title

Proceedings of the American Mathematical Society

Volume

139

Issue

8

Number of Pages

2671-2680

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1090/S0002-9939-2011-10719-6

Socpus ID

79955763142 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/79955763142

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