This article is cited in 8 papers


Series of articles on the multioperator rings and algebras
Multioperator algebras and clones of polylinear operators

V. A. Artamonov


Abstract: 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.

UDC: 519.4+519.9

MSC: 47H60, 47C05, 47S10

Received: 30.09.1968

 English version: Russian Mathematical Surveys, 1969, 24:1, 45–57

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