"Computation of standard bases of ideals of free noncommutative
 algebras"

A.A.Mikhalev* and A.A.Zolotykh
Moscow State University, Russia,
aamikh@cnit.math.msu.su zolotykh@lsili.ru

Abstract:

We consider standard bases of free Lie algebras and free associative
algebras over rings. The main result is a criterion for a subset
of a free algebra to be a standard basis of the ideal it generates.
Based on this result we present algorithms to construct standard bases
and discuss the termination condition for these algorithms.