Abstract In this article, we define the following: Let N 0 {{\mathbb{N}}}_{0} be set of all nonnegative integers and D = ( d i ) ∈ D={\left({d}_{i})}_...

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.

In this paper we study the properties of derivations of A B, where A and B are simple separable C*-algebras, and A B is the C*-completion of A B with respect to a C*-norm Yon A B and we will characterize the derivations of A B in terms of the derivations of A and B

recently, the algebraic theory of mv -algebras is intensively studied. in this paper, we extend the concept of derivation of $mv$-algebras and we give someillustrative examples. moreover, as a generalization of derivations of $mv$ -algebraswe introduce the notion of $f$-derivations and $(f; g)$-derivations of $mv$-algebras.also, we investigate some properties of them.

The multidimensional chain rule formula for analytic functions and its generalisation to higher derivatives perfectly work in the algebraic setting in characteristic zero. In positive characteristic one runs into problems due to denominators in these formulas. In this article we show a direct analog of these formulas using higher derivations which are defined in any characteristic. We also use ...