In this study, we define the generalized symmetric bi-derivation and its trace on MV-algebras give examples. We investigate some properties of bi-derivation’s trace. introduce isotone bi-additive bi-derivation. show that if A is a linearly ordered MV-algebra, Γ related to D γ , then = 0 or γ1 1

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.