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TitleGröbner bases of ideals invariant under endomorphisms
Author(s) Vesselin Drensky, Roberto La Scala
TypeArticle in Journal
AbstractWe introduce the notion of Gröbner S -basis of an ideal of the free associative algebra K〈X〉 over a field K invariant under the action of a semigroup S of endomorphisms of the algebra. We calculate the Gröbner S -bases of the ideal corresponding to the universal enveloping algebra of the free nilpotent of class 2 Lie algebra and of the T-ideal generated by the polynomial identity [x, y, z] = 0 , with respect to suitable semigroups S . In the latter case, if |X| > 2 , the ordinary Gröbner basis is infinite and our Gröbner S -basis is finite. We obtain also explicit minimal Gröbner bases of these ideals.
KeywordsFree algebras, Gröbner bases, Algebras with polynomial identity, Grassmann algebra, Universal enveloping algebras
URL http://www.sciencedirect.com/science/article/pii/S0747717106000228
JournalJournal of Symbolic Computation
Pages835 - 846
Translation No
Refereed No