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arXiv · 0710.4945

Degree Bounds for Gröbner Bases in Algebras of Solvable Type

Matthias Aschenbrenner·Anton Leykin
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Abstract

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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Matthias Aschenbrenner, Anton Leykin. 2008-11-19. Degree Bounds for Gröbner Bases in Algebras of Solvable Type. https://arxiv.org/abs/0710.4945

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