|
Organizers |
Functional identities and generalized functional
by
Matej Bresar
University of Maribor
The talk will give a short introduction to a new theory, the theory of functional identities and generalized functional identities in (mainly prime) rings. Roughly speaking, functional identities are identities involving arbitrary maps of the ring; if such identities also involve some fixed elements in the ring, then we talk about generalized functional identities. The concept of functional identities can be viewed as a generalization of the concept of polynomial identities, while the concept of generalized functional identities extends the concept of generalized polynomial identities. The usual goal in the consideration of (generalized) functional identities is to find either the form of the maps involved or to establish some structural properties of the ring.
This theory has turned out to be applicable to different problems. In particular, long-standing Herstein's conjectures concerning Lie isomorphisms of associative rings have been proved using functional identities.
The study of (generalized) functional identities has been initiated in the beginning of the 90's by the author in the series of papers. After that, several mathematicians have given contributions to the theory. However, we have to point out the important role of K. I. Beidar in developing the theory of functional identities, and a similar role of M. A. Chebotar concerning generalized functional identities.
Date received: November 2, 1998
Copyright © 1998 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cabw-05.