f q -Derivations of G -Algebra

Abstract EN

We introduce the notion of f q -derivation as a new derivation of G -algebra.

For an endomorphism map f of any G -algebra X , we show that at least one f q -derivation of X exists.

Moreover, for such a map, we show that a self-map d q f of X is f q -derivation of X if X is an associative medial G -algebra.

For a medial G -algebra X , d q f is f q -derivation of X if d q f is an outside f q -derivation of X .

Finally, we show that if f is the identity endomorphism of X then the composition of two f q -derivations of X is a f q -derivation.

Moreover, we give a condition to get a commutative composition.