STANDARD BASES IN K[[t1,..., tm]][x1,...,xn] s
نویسنده
چکیده
Abstract. In this paper we study standard bases for submodules of K[[t1, . . . , tm]][x1, . . . , xn] s respectively of their localisation with respect to a t-local monomial ordering. The main step is to prove the existence of a division with remainder generalising and combining the division theorems of Grauert and Mora. Everything else then translates naturally. Setting either m = 0 or n = 0 we get standard bases for polynomial rings respectively for power series rings as a special case. We then apply this technique to show that the t-initial ideal of an ideal over the Puiseux series field can be read of from a standard basis of its generators. This is an important step in the constructive proof that each point in the tropical variety of such an ideal admits a lifting.
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