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Relative MV-algebras and relative homomorphisms

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Mathematica Slovaca

Abstract

In this paper we define the notion of relative subalgebra of an MV-algebra A. A particular case of this notion is the notion of interval subalgebra of A; this has been already studied in the literature.

Applying these notions, two new categories denoted as r

and int

are introduced. In both cases the objects are MV-algebras, but the homomorphisms are defined by means of relative subalgebras or by interval subalgebras, respectively. The relations occurring between these categories and the category of all MV-algebras with usual homomorphisms are investigated. The main results of the paper deal with one-generated free MV-algebras in the variety generated by the finite chains S i , i ⩽ p (p varying over the set of all positive integers) and their relations to certain relative subalgebras of the cyclic free MV-algebra.

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Authors and Affiliations

  1. Department of Mathematics and Informatics, University of Salerno, Via Ponte don Melillo, I-84084, Fisciano, Salerno, Italy

    Antonio Di Nola

  2. Dipartimento di Costruzioni e Metodi Matematici in Architettura, University of Naples Federico II, I-80134, Naples, Italy

    Ada Lettieri

Authors
  1. Antonio Di Nola
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  2. Ada Lettieri
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Correspondence to Antonio Di Nola.

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Communicated by Anatolij Dvurečenskij

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Di Nola, A., Lettieri, A. Relative MV-algebras and relative homomorphisms. Math. Slovaca 60, 43–64 (2010). https://doi.org/10.2478/s12175-009-0166-8

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  • DOI: https://doi.org/10.2478/s12175-009-0166-8

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