Degree Bounds for Gröbner Bases in Algebras of Solvable Type
| dc.creator | Aschenbrenner, Matthias | |
| dc.creator | Leykin, Anton | |
| dc.date | 2007-10-25 | |
| dc.date | 2008-11-19 | |
| dc.date.accessioned | 2026-07-07T10:18:55Z | |
| dc.date.available | 2026-07-07T10:18:55Z | |
| dc.description | 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). | |
| dc.description | 36 pages; typos corrected | |
| dc.identifier | https://arxiv.org/abs/0710.4945 | |
| dc.identifier | http://arxiv.org/abs/0710.4945 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/174358 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Rings and Algebras | |
| dc.subject | 13P10, 16Z05 | |
| dc.title | Degree Bounds for Gröbner Bases in Algebras of Solvable Type | |
| dc.type | text |