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Title  Tropical Noetherity and Groebner bases  Author(s)  Ya KAZARNOVSKI ̆, A. G. KHOVANSKI ̆  Type  Article in Journal  Abstract  A 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.
 Keywords  Laurent polynomial, ideal, tropical basis, universal Groebner basis, Seidenberg theorem 
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 Language  English  Journal  St. Petersburg Math. J.  Volume  26  Number  5  Year  2014  Edition  0  Translation 
No  Refereed 
No 
