We show that the structure of continuous and discontinuous homomorphisms from the Banach algebra Cn[0,1] of n times continuously differentiable functions on the unit interval [0,1] into finite dimensional Banach algebras is completely determined by higher point derivations.

In this paper, we consider Leibniz algebras with derivations. A pair consisting of a algebra and distinguished derivation is called LeibDer pair. We define cohomology theory for coefficients in representation. study central extensions the next, generalize formal deformation to pairs which deform both bracket derivation. It governed by itself. Finally, homotopy derivations on sh 2-derivations 2-...

In this paper we introduce derivations in Krasner hyperrings and derive some basic properties of derivations. We also prove that for a strongly differential hyperring $R$ and for any strongly differential hyperideal $I$ of $R,$ the factor hyperring $R/I$ is a strongly differential hyperring. Further we prove that a map $d: R rightarrow R$ is a derivation of a hyperring $R$ if and only if the in...

In this paper, we introduce the notions of (l, r)-derivations, (r, l)-derivations, and derivations Hilbert algebras investigate some related properties. addition, define two subsets for a derivation d algebra X, Ker d(X) Fix d(X), also take look at their characteristics.