Tropical noetherity and Gröbner bases

Kazarnovskiĭ, Ya.; Khovanskiĭ, A.

doi:10.1090/spmj/1359

Tropical noetherity and Gröbner bases
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by Ya. Kazarnovskiĭ and A. G. Khovanskiĭ
Translated by: B. M. Bekker

St. Petersburg Math. J. 26 (2015), 797-811

DOI: https://doi.org/10.1090/spmj/1359

Published electronically: July 27, 2015

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Abstract:

A set that is a Gröbner basis for an ideal with respect to every Gröbner ordering is called a universal Gröbner basis for that ideal. In the paper, it is proved that there exists a universal Gröbner 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 $(\mathbb {C}^*)^n$, which will be presented in a forthcoming paper.

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