Home | Quick Search | Advanced Search | Bibliography submission | Bibliography submission using bibtex | Bibliography submission using bibtex file | Links | Help | Internal

Details:

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

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".
LanguageEnglish
Pages150-161
Year1988
Edition0
Translation No
Refereed No
Webmaster