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TitleGroebner Bases in Non-Commutative Algebras
Author(s) Ferdinando Mora
TypeArticle in Conference Proceedings

Recently, the use of Groebner bases and Buchberger algorithm [BUC1,2,4] has been generalised from the case of commutative polynomials to finitely generated algebras R over a field k, R = k<Xl,...,Xn>, s.t. for each i < j, for some cij ( k, for some commutative polynomial Pij ( k[Xl,...,Xn], one has xj xi - cij xi xj = Pij(Xl,...,Xn).

The first results in this direction were due to Galligo [GAL], which studied Groebner bases for left ideals in Weyl algebras (R = k<x 1 ,...,xn,dl ,...,dn> with di xi - xi di = 1 for each i, di xj = xj di, xi xj = xj xi, di dj = dj di if i j); and to Apel - Lassner [A-L], which studied Groebner bases for left ideals in tensor algebras over Lie algebras (cij = 1, Pij linear).

Kandri-Rody - Weispfenning [KRW] were the first to study Groebner bases for two-sided ideals, in "solvable polynomial rings".
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Refereed No