FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2000, VOLUME 6, NUMBER 3, PAGES 669-706

Gröbner and Gröbner--Shirshov bases in algebra and conformal algebras

L. A. Bokut'
Yu. Fong
W.-F. Ke
P. S. Kolesnikov

Abstract

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In this paper the Gröbner--Shirshov bases theory is regularly presented for commutative, non-commutative, Lie and conformal algebras. The general form of Composition-Diamond lemma for conformal relations is stated. We have made a review of some results obtained with Gröbner--Shirshov bases of usual and conformal algebras. It is proved that every finitely generated commutative conformal algebra is Noetherian, an analogue of Specht problem is considered for commutative conformal algebras.

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Last modified: December 8, 2000