the notion of $f$-derivations of up-algebras is introduced, some useful examples are discussed, and related properties are investigated. moreover, we show that the fixed set and the kernel of $f$-derivations are up-subalgebras of up-algebras,and also give examples to show that the two sets are not up-ideals of up-algebras in general.

The equivalence principle is treated on a mathematically rigorous base on sufficiently general subsets of a differentiable manifold. This is carried out using the basis of derivations of the tensor algebra over that manifold. Necessary and/or sufficient conditions of existence, uniqueness, and holonomicity of these bases in which the components of the derivations of the tensor algebra over it v...

The main purpose of this research is to characterize generalized (left) derivations and Jordan (*,*)-derivations on Banach algebras rings using some functional identities. Let A be a unital semiprime algebra let F,G : ? linear mappings satisfying F(x) =-x2G(x-1) for all x Inv(A), where Inv(A) denotes the set invertible elements A. Then both F G are Another result in regard as follows. n > 1 ...