Degree Bounds for Gröbner Bases in Algebras of Solvable Type

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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).
36 pages; typos corrected

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Commutative Algebra, Rings and Algebras, 13P10, 16Z05

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http://salesiana.dossiersoluciones.com/handle/123456789/174358

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0710.4945
 http://arxiv.org/abs/0710.4945

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arXiv