Mikhail A. Chebotar

On Herstein’s Lie map conjectures, I

First published in Transactions- American Mathematical Society in Vol.353, No.10, pp.4235-4260, published by the American Mathematical Society

FUNCTIONAL IDENTITIES REVISED: THE FRACTIONAL AND THE STRONG DEGREE

ABSTRACT The concepts of the fractional and the strong degree of an element in a ring are introduced. It is shown that definitive results on functional identities can be obtained in rings which contain elements of appropriate fractional (or strong) degree. This enables us to extend the results on functional identities from prime to semiprime rings, as well as to some rather different classes of rings, such as matrix rings over any unital ring. As an application, commuting maps, Lie derivations and commutativity preserving maps in such rings are discussed.

Functional identities on upper triangular matrix algebras

AbstractLet

A NOTE ON DERIVATIONS, ADDITIVE SUBGROUPS, AND LIE IDEALS OF PRIME RINGS

\tau _r ,r \geqslant 2

A Note on Polynomial Rings over Nil Rings

, be the algebra of upper triangular r×r matrices over field aF. We describe multilinear maps

L-prime rings need not be primary

f:\tau _r^n \to \tau _r