Non-associative Gröbner bases

Rajaee, Saeed

doi:10.1016/j.jsc.2006.04.005

Cited by 6 publications

(2 citation statements)

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“…The most important branch of the nonassociative theory deals with Gröbner-Shirshov bases for free Lie algebras; see Bokut and Chibrikov [19] and Bokut and Chen [13]. A theory of Gröbner-Shirshov bases in free nonassociative algebras has been developed by Gerritzen [53,54] and Rajaee [95]. For related work on Sabinin algebras, see Shestakov and Umirbaev [97], Pérez-Izquierdo [92], and Chibrikov [39].…”

Section: Bibliographical Remarksmentioning

confidence: 99%

Free associative algebras, noncommutative Grobner bases, and universal associative envelopes for nonassociative structures

Bremner

2013

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The underlying motivation is to apply the theory of noncommutative Gröbner bases in free associative algebras to the construction of universal associative envelopes for nonassociative structures defined by multilinear operations. Trilinear operations were classified by the author and Peresi in 2007. In her Ph.D. thesis of 2012, Elgendy studied the universal associative envelopes of nonassociative triple systems obtained by applying these trilinear operations to the 2-dimensional simple associative triple system. In these notes I use computer algebra to extend some aspects of her work to the 4-dimensional and 6-dimensional simple associative triple systems.

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Section: Bibliographical Remarksmentioning

confidence: 99%

Free associative algebras, noncommutative Grobner bases, and universal associative envelopes for nonassociative structures

Bremner

2013

Preprint

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“…Recently Gröbner bases in general non-associative algebras have been studied (see e.g., [3], [5], [13]). In this paper we use these to deal with finitely-presented Lie rings.…”

Section: Introductionmentioning

confidence: 99%