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TitleTropical Noetherity and Groebner bases
Author(s) Ya KAZARNOVSKI ̆, A. G. KHOVANSKI ̆
TypeArticle in Journal
AbstractA set that is a Groebner basis for an ideal with respect to every Groebner ordering is called a universal Groebner basis for that ideal. In the paper, it is proved that there exists a universal Groebner basis in which the polynomials have controlled degrees. The main result is the theorem on the tropical Noetherity of a ring of Laurent polynomials. This theorem is close to the existence theorem for a universal basis and is needed for the tropical intersection theory in (C∗ )n , which will be presented in a forthcoming paper.
KeywordsLaurent polynomial, ideal, tropical basis, universal Groebner basis, Seidenberg theorem
File
LanguageEnglish
JournalSt. Petersburg Math. J.
Volume26
Number5
Year2014
Edition0
Translation No
Refereed No
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