ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 16, 17 Zolotykh, Andrej A., Moscow State University, Russia, Mikhalev, Alexander A., Moscow State University, Russia Standard bases for ideals of free algebras over commutative rings Standard Gröbner-Shirshov bases of ideals of free associative algebras and free (super)algebras over finitely generated commutative rings are under consideration. The main result is a criterion for a subset of free algebras to be a standard basis (reduced standard basis) of the ideal it generates. We obtain also an infinite algorithm to construct standard bases of ideals. Reference: A. A. Mikhalev, and A. A. Zolotykh, Standard Gröbner-Shirshov bases of free algebras over rings, I. Free associative algebras, Int. J. Algebra Comput. , in press.