ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 16 Vasilieva, Ekaterina A., University of Moscow, Russia Involutive Bases of Free Algebras M. Janet [1] and J. F. Pommaret [2] used involutive approach in solving systems of differential equations. A. Yu. Zharkov, Yu. A. Blinkov [3] and V. P. Gerdt [4] studied involutive bases of ideals of polynomial algebras. We proved a criterion for a subset of an ideal of a free associative algebra to be the involutive basis of this ideal. References:

[1] Janet M. Sur les Systemes d’Equations aux Dérivées Partielles. J. Math. Pure et Appl. 3, 65–151.

[2] Pommaret J. F. Systems of Partial Differential Equations and Lie Pseudogroups. Gordon & Breach, New York.

[3] Zharkov A. Yu, Blinkov Yu. A. Involutive Approach to Investigating Polynomial Systems. In: Math. Comp. Simul 42 (1996), 323–332.

[4] Gerdt V. P. Gröbner Bases and Involutive Methods for Algebraic and Differential Equations. In: Computer Algebra in Science and Engineering, 117–137.