Standard Bases in Kt 1,...,t mx 1,...,x n^s - Mathematics > Commutative AlgebraReport as inadecuate




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Abstract: In this paper we study standard bases for submodules ofKt 1,

.,t mx 1,

.,x n^s respectively of their localisation with respectto a t-local monomial ordering. The main step is to prove the existence of adivision with remainder generalising and combining the division theorems ofGrauert and Mora. Everything else then translates naturally. Setting either m=0or n=0 we get standard bases for polynomial rings respectively for power seriesrings as a special case. We then apply this technique to show that thet-initial ideal of an ideal over the Puiseux series field can be read of from astandard basis of its generators. This is an important step in the constructiveproof that each point in the tropical variety of such an ideal admits alifting.



Author: Thomas Markwig

Source: https://arxiv.org/



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