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

Research output: Contribution to journal › Article › peer-review

69 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	50-75
Number of pages	26
Journal	Communications in Algebra
Volume	39
Issue number	1
DOIs	https://doi.org/10.1080/00927870903431209
State	Published - 2010
Externally published	Yes

Keywords

Buchberger's algorithm
Noetherian polynomial noncommutative rings
Noncommutative Gröbner bases
PBW extensions

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10.1080/00927870903431209

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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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AU - Lezama, Oswaldo

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AB - 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.

KW - Buchberger's algorithm

KW - Noetherian polynomial noncommutative rings

KW - Noncommutative Gröbner bases

KW - PBW extensions

UR - https://www.scopus.com/pages/publications/78951479386

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DO - 10.1080/00927870903431209

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VL - 39

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JO - Communications in Algebra

JF - Communications in Algebra

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ER -

Gröbner bases for ideals of σ-PBW extensions

Abstract

Keywords

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