Multioperator algebras and clones of polylinear operators

In this paper we consider principal derived polylinear operators on an $\Omega$-algebra $A$ over an infinite field $P$. We clarify them in terms of partial algebras, that is, of clones. The classification allows us also to classify the multioperator structures on a vector space $A$ for various systems of multioperators.
The idea of discussing clones comes from Cohn's book [1] and the papers of Whitlock [2], Khion [3] and Dicker [4]. We also use certain concepts of Higgins [5] relating to partial algebras.
The author expresses his sincere thanks to A. G. Kurosh for his guidance on this work.