Groebner bases of ideals invariant under endomorphisms

Details Groebner bases of ideals invariant under endomorphisms Groebner bases of ideals invariant under endomorphisms

2005-10-27

arxiv.org/abs/math/0510589v2

Journal of Symbolic Computation 41 (2006), No. 7, 835-846.

Mathematics

Rings and Algebras

15 pages

Scientific paper

10.1016/j.jsc.2006.04.004

We introduce the notion of Groebner S-basis of an ideal of the free associative algebra K over a field K invariant under the action of a semigroup S of endomorphisms of the algebra. We calculate the Groebner 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 Groebner basis is infinite and our Groebner S-basis is finite. We obtain also explicit minimal Groebner bases of these ideals.

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