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Fregean subtractive varieties with definable congruence

Part of: Algebraic structures

Published online by Cambridge University Press:  09 April 2009

Paolo Agliano
Paolo Agliano
Affiliation:
Dipartimento di Matematica, Via del Capitano 15, 53100, Siena, Italy e-mail: [email protected]
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Abstract

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In this paper we investigate subtractive varieties of algebras that are Fregean in order to get structure theorems about them. For instance it turns out that a subtractive variety is Fregean and has equationally definable principal congruences if and only if it is termwise equivalent to a variety of Hilbert algebras with compatible operations. Several examples are provided to illustrate the theory.

Keywords

Fregeansubtractive varietydefinable congruences

MSC classification

Secondary: 08A99: None of the above, but in this section 08A30: Subalgebras, congruence relations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 71 , Issue 3 , December 2001 , pp. 353 - 366
Copyright
Copyright © Australian Mathematical Society 2001

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