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Hyperidentities

  • Chapter
Algebras and Orders

Part of the book series: NATO ASI Series ((ASIC,volume 389))

Abstract

If one considers free algebras as semigroups of composition of terms or more specifically as clones of terms, the identities of these semigroups (respectively clones) can be interpreted as hyperidentities. Hyperidentities contain hypervariables which stand for terms, and describe the manipulation of these terms. We present a logic for hyperidentities and more generally for hybrid identities, a completeness theorem and deal with solid varieties. Separating hyperidentities for various semigroups and clones are presented next. The congruences of free algebras and of the clones of terms are described. Furthermore, many open questions and problems are included.

Dla Magdy, Dagusi i Krzysia

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  1. Mathematisches Institut, Universität Kaiserslautern, DW-6750, Kaiserslautern, Germany

    Dietmar Schweigert

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  1. Dietmar Schweigert
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  1. Département de mathématiques et de statistique, Université de Montréal, C.P. 6128, Succ. A, H3C 3J7, Montréal, Québec, Canada

    Ivo G. Rosenberg (Scientific Director of the ASI) & Gert Sabidussi (Scientific Director of the ASI) & 

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Schweigert, D. (1993). Hyperidentities. In: Rosenberg, I.G., Sabidussi, G. (eds) Algebras and Orders. NATO ASI Series, vol 389. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0697-1_10

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