Degree Bounds for Gröbner Bases in Algebras of Solvable Type

Details Degree Bounds for Gröbner Bases in Algebras of Solvable Type Degree Bounds for Gröbner Bases in Algebras of Solvable Type

2007-10-25

arxiv.org/abs/0710.4945v5

Mathematics

Commutative Algebra

36 pages; typos corrected

Scientific paper

We establish doubly-exponential degree bounds for Gr\"obner 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 Dub\'e 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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