Let R be a prime ring of characteristic different from 2, U the Utumi quotient ring of R, C the extended centroid of R, F and G non-zero generalized derivations of R. If the composition (FG) acts as a Lie derivation on R, then (FG) is a derivation of R and one of the following holds: 1. there exist α ∈ C and a ∈ U such that F (x) = [a, x] and G(x) = αx, for all x ∈ R; 2. G is an usual derivatio...

The group properties of the shallow-water equations with complete Coriolis force is subject this study. In particular we apply Lie theory to classify system three nonlinear partial differential according admitted point symmetries. For each case classification problem one-dimensional optimal determined. results are applied for derivation new similarity solutions.

We classify all the pairs of a commutative associative algebra with an identity element and its finite-dimensional commutative locally-finite derivation subalgebra such that the commutative associative algebra is derivation-simple with respect to the derivation subalgebra over an algebraically closed field with characteristic 0. Such pairs are the fundamental ingredients for constructing genera...

In this note we propose a definition of inner derivation for nonassociative algebras. This definition coincides with the usual one for Lie algebras, and for associative algebras with no absolute right (left) divisor of zero. I t is well known that all derivations of semi-simple associative or Lie algebras over a field of characteristic zero are inner. Recent correspondence with N. Jacobson has ...

It is proved that the derivation algebra of a centerless perfect Lie algebra of arbitrary dimension over any field of arbitrary characteristic is complete and that the holomorph of a centerless perfect Lie algebra is complete if and only if its outer derivation algebra is centerless. Key works: Derivation, complete Lie algebra, holomorph of Lie algebra Mathematics Subject Classification (1991):...