NOETHER NORMALIZATIONS, REDUCTIONS OF IDEALS, AND MATROIDS

    Authors

    J. P. Brennan;N. Epstein

    Comments

    Authors: contact us about adding a copy of your work at [email protected]

    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

    Language

    English

    First Page

    2671

    Last Page

    2680

    WOS Identifier

    WOS:000292623900003

    ISSN

    0002-9939

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