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Semi-Nelson Algebras

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Abstract

Generalizing the well known and exploited relation between Heyting and Nelson algebras to semi-Heyting algebras, we introduce the variety of semi-Nelson algebras. The main tool for its study is the construction given by Vakarelov. Using it, we characterize the lattice of congruences of a semi-Nelson algebra through some of its deductive systems, use this to find the subdirectly irreducible algebras, prove that the variety is arithmetical, has equationally definable principal congruences, has the congruence extension property and describe the semisimple subvarieties.

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  1. Instituto de Matemática de Bahía Blanca, Universidad Nacional del Sur-CONICET, Departamento de Matemática -, Av. Alem 1253, Bahía Blanca, Buenos Aires, Argentina

    Juan Manuel Cornejo & Ignacio Viglizzo

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  1. Juan Manuel Cornejo
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  2. Ignacio Viglizzo
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Correspondence to Ignacio Viglizzo.

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Cornejo, J.M., Viglizzo, I. Semi-Nelson Algebras. Order 35, 23–45 (2018). https://doi.org/10.1007/s11083-016-9416-x

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