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Menger Algebras and Clones of Cooperations

Klaus Denecke

Universität Potsdam, Institut für Mathematik, Am Neuen Palais, 14415 Potsdam, Germany

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and

Kittisak Saengsura

Universität Potsdam, Institut für Mathematik, Am Neuen Palais, 14415 Potsdam, Germany

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https://doi.org/10.1142/S1005386708000229Cited by:3 (Source: Crossref)

Abstract

The superposition of cooperations satisfies the well-known clone axioms (C1), (C2) and (C3). We define terms for indexed coalgebras of type τ, cooperations induced by those terms, and prove that the set of all induced cooperations forms a clone. This clone is equal to the clone of all cooperations generated by the fundamental cooperations of an indexed coalgebra. Finally, we introduce the concept of rational equivalence for coalgebras and determine all two-element coalgebras up to rational equivalence.

Keywords:

AMSC: 68Q55, 08A40

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