Clones of modes
by
Norbert Dojer
Warsaw University

The aim of this presentation is to indicate some applications of techniques derived from the theory of clones and hyperidentities to the theory of modes. Since idempotent and entropic laws hold for derived operations provided they do for basic ones, a class of all modes (of any type) is definable by a set of hyperidentities. Therefore studying such applications seems to be profitable for exploring the theory of modes as well as illustrating the possibilities and elegance of the theory of clones and hypervarieties.

The main result of the presentation is a characterization of a class of linear modes, i.e. modes satisfying certain set of hyperidentities (linear modes form a really wide class, including all modes investigated as yet).

Date received: May 19, 2004