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García García, Juan Ignacio; García Miranda, Jesus; Lobillo, F. J.

Elimination orderings and localization in PBW algebras. (English) Zbl 1213.16039

Linear Algebra Appl. 430, No. 8-9, 2133-2148 (2009).
Summary: We characterize the existence of elimination orderings for a given PBW algebra. Elimination orderings on \(\mathbb{N}^p\) are analyzed. A subclass of elimination orderings is considered to handle some Ore subsets and classical localizations.

Cited in 1 Review
Cited in 3 Documents

MSC:

16Z05 Computational aspects of associative rings (general theory)
16S15 Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting)
16S85 Associative rings of fractions and localizations
20M14 Commutative semigroups
16U20 Ore rings, multiplicative sets, Ore localization
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)

Keywords:

PBW algebras; monomial orderings; elimination orderings; Ore sets; Weyl algebras; quantum spaces; quantum enveloping algebras

Citations:

Zbl 1172.20311

Software:

Plural; SINGULAR; nctools.lib
Cite Review PDF
Full Text: DOI

References:

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