Abstract We define a new notion of fiberwise linear differential operator on the total space vector bundle E . Our main result is that operators are equivalent to (polynomial) derivations an appropriate line over E ? {E^{\ast}} believe this might represent first step towards definition m...

The aim of this paper is to show that under some mild conditions a functional equation of multiplicative $(alpha,beta)$-derivation is superstable on standard operator algebras. Furthermore, we prove that this generalized derivation can be a continuous and an inner $(alpha,beta)$-derivation.

In this paper, we address the additivity of n-multiplicative isomorphisms and derivations on gamma rings. We proved that, if $${{\mathfrak {M}}}\, $$ is a $$\Gamma -ring satisfying some conditions, then any isomorphism $$\left( \varphi , \phi \right) onto an arbitrary ring additive.

In this paper, we modify the result of M. N. Daif [1] on multiplicative derivations in rings. He showed that derivation is additive by imposing certain conditions ring ℜ. Here, have proved above with lesser than for getting to be additive.

We study the endomorphisms and derivations of an infinite-dimensional cyclic Leibniz algebra. Among others it was found that if [Formula: see text] is a algebra over field text], then group all automorphisms isomorphic to multiplicative text]. The description has been obtained.

Nonsingular derivations of modular Lie algebras which have finite multiplicative order play a role in the coclass theory for pro-p groups and Lie algebras. A study of the set Np of positive integers which occur as orders of nonsingular derivations of finite-dimensional non-nilpotent Lie algebras of characteristic p > 0 was initiated by Shalev and continued by the present author. In this paper w...