Details:
Title  Gröbner bases of ideals invariant under endomorphisms  Author(s)  Vesselin Drensky, Roberto La Scala  Type  Article in Journal  Abstract  We 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 Tideal 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.  Keywords  Free algebras, Gröbner bases, Algebras with polynomial identity, Grassmann algebra, Universal enveloping algebras  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717106000228 
Language  English  Journal  Journal of Symbolic Computation  Volume  41  Number  7  Pages  835  846  Year  2006  Edition  0  Translation 
No  Refereed 
No 
