In the present paper, we prove that every local and $2$-local derivation of complex finite-dimensional simple Filippov algebra is a derivation. As corollary have description all derivations semisimple algebras. All ternary Malcev $M_8$ are described. It first example admits pure derivations, i.e. which not

Ternary stress presents a unique challenge to constraint-based metrical stress theories. The main question is how to model ternarity without ternary-specific representations, such as ternary feet. Along this line of reasoning, Elenbaas and Kager (1999) interpret ternarity as an underparsing effect in which long lapses are avoided while the number of feet is kept to a minimum. The standard const...

The main goal of this paper is to introduce the notion 3-L-dendriform algebras which are dendriform version 3-pre-Lie algebras. In fact they algebraic structures behind O-operator They can be also regarded as ternary analogous L-dendriform Moreover, we study generalized derivations Finally, explore spaces quasi-derivations, centroids and quasi-centroids give some properties.

Let  be a Banach algebra. Let  be linear mappings on . First we demonstrate a theorem concerning the continuity of double derivations; especially that all of -double derivations are continuous on semi-simple Banach algebras, in certain case. Afterwards we define a new vocabulary called “-higher double derivation” and present a relation between this subject and derivations and finally give some ...