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Isometries and direct product decompositions of GMV-algebras

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Mathematica Slovaca

Abstract

We apply the concept of generalized MV-algebra (GMV-algebra, for short) in the sense defined and studied by Galatos and Tsinakis. We introduce the notion of isometry of a GMV-algebra; we investigate the relations between isometries and direct product decompositions of GMV-algebras. Using these relations we show that if a GMV-algebra M has a greatest element, then each isometry of M is idempotent.

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Authors and Affiliations

  1. Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, SK-040 01, Košice, Slovakia

    Ján Jakubík

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  1. Ján Jakubík
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Correspondence to Ján Jakubík.

Additional information

Communicated by Anatolij Dvurečenskij

Dedicated to Professor Sylvia Pulmannová on the occasion of her 70th birthday

This work was supported by the Slovak Research and Development Agency under the contract No APVV-0071-06.

This work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence — Physics of Information (grant I/2/2005).

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Jakubík, J. Isometries and direct product decompositions of GMV-algebras. Math. Slovaca 60, 591–606 (2010). https://doi.org/10.2478/s12175-010-0034-6

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  • DOI: https://doi.org/10.2478/s12175-010-0034-6

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