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A Characterization of P-Compatible Varieties

Ivan Chajda

Department of Algebra and Geometry, Palacký University, Tomkova 40, 779 00 Olomouc, Czech Republic

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Klaus Denecke

University of Potsdam, Institute of Mathematics, Am Neuen Palais, 14415 Potsdam, Germany

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, and

Shelly L. Wismath

Department of Mathematics and Computer Science, University of Lethbridge, 4401 University Drive, Lethbridge, Ab., T1K-3M4, Canada

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https://doi.org/10.1142/S1005386707000193Cited by:1 (Source: Crossref)

Abstract

P-Compatibility is a hereditary property of identities which generalizes the properties of normality and externality of identities. Chajda characterized the normalization of a variety by an algebraic construction called a choice algebra. In this paper, we generalize this characterization to the least P-compatible variety P(V) determined by a variety V for any partition P using P-choice algebras. We also study the clone of (strongly) P-compatible n-ary terms of a variety V, and relate identities of this clone to (strongly) P-compatible hyperidentities of the variety V.

Research of the third author was supported by NSERC of Canada.

Keywords:

AMSC: 08A40, 08A60, 08A02, 08B05

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