Gröbner bases for ideals of σ-PBW extensions

Claudia Gallego; Oswaldo Lezama

doi:10.1080/00927870903431209

Gröbner bases for ideals of σ-PBW extensions

Claudia Gallego, Oswaldo Lezama

Producción: Contribución a una revista › Artículo › revisión exhaustiva

63 Citas (Scopus)

Resumen

In this article, we introduce the σ-PBW extensions and construct the theory of Gröbner bases for the left ideals of them. We prove the Hilbert's basis theorem and the division algorithm for this more general class of Poincaré-Birkhoff-Witt extensions. For the particular case of bijective and quasi-commutative σ-PBW extensions, we implement the Buchberge's algorithm for computing Gröbner bases of left ideals.

Idioma original	Inglés
Páginas (desde-hasta)	50-75
Número de páginas	26
Publicación	Communications in Algebra
Volumen	39
N.º	1
DOI	https://doi.org/10.1080/00927870903431209
Estado	Publicada - 2010
Publicado de forma externa	Sí

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abstract = "In this article, we introduce the σ-PBW extensions and construct the theory of Gr{\"o}bner bases for the left ideals of them. We prove the Hilbert's basis theorem and the division algorithm for this more general class of Poincar{\'e}-Birkhoff-Witt extensions. For the particular case of bijective and quasi-commutative σ-PBW extensions, we implement the Buchberge's algorithm for computing Gr{\"o}bner bases of left ideals.",

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KW - Buchberger's algorithm

KW - Noetherian polynomial noncommutative rings

KW - Noncommutative Gröbner bases

KW - PBW extensions

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Gröbner bases for ideals of σ-PBW extensions

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