可解型代数中Gröbner基的度界
Degree Bounds for Gröbner Bases in Algebras of Solvable Type
摘要：
我们建立了域上可解型代数中Gröbner基的双指数度界（由Kandri-Rody和Weispfenning引入）。这里考虑的代数类包括交换多项式环、Weyl代数和有限维李代数的泛包络代数。对于这些界限的计算，我们适应的方法，由于Dubé的基础上推广的斯坦利分解。我们的界限产生双指数度界限的理想成员和syzygies，推广的经典结果赫尔曼和塞登伯格（在交换的情况下）和格里戈里耶夫（在Weyl代数的情况下）。
英文摘要：
We establish doubly-exponential degree bounds for Gröbner bases in certain algebras of solvable type over a field (as introduced by Kandri-Rody and Weispfenning). The class of algebras considered here includes commutative polynomial rings, Weyl algebras, and universal enveloping algebras of finite-dimensional Lie algebras. For the computation of these bounds, we adapt a method due to Dubé based on a generalization of Stanley decompositions. Our bounds yield doubly-exponential degree bounds for ideal membership and syzygies, generalizing the classical results of Hermann and Seidenberg (in the commutative case) and Grigoriev (in the case of Weyl algebras).
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