Title

NOETHER NORMALIZATIONS, REDUCTIONS OF IDEALS, AND MATROIDS

Authors

Authors

J. P. Brennan;N. Epstein

Comments

Authors: contact us about adding a copy of your work at STARS@ucf.edu

Abbreviated Journal Title

Proc. Amer. Math. Soc.

Keywords

BRIANCON-SKODA THEOREM; JOINT REDUCTIONS; TIGHT CLOSURE; GRAPHS; MULTIPLICITIES; ALGEBRAS; RINGS; Mathematics, Applied; Mathematics

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.

Journal Title

Proceedings of the American Mathematical Society

Volume

139

Issue/Number

8

Publication Date

1-1-2011

Document Type

Article

DOI Link

http://dx.doi.org/10.1090/s0002-9939-2011-10719-6

Language

English

First Page

2671

Last Page

2680

WOS Identifier

WOS:000292623900003

ISSN

0002-9939

Recommended Citation

"NOETHER NORMALIZATIONS, REDUCTIONS OF IDEALS, AND MATROIDS" (2011). Faculty Bibliography 2010s. 1121.
https://stars.library.ucf.edu/facultybib2010/1121