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Soft Computing

, Volume 21, Issue 21, pp 6213–6223 | Cite as

Notes on divisible MV-algebras

Foundations

Abstract

In this notes, we study the class of divisible MV-algebras inside the algebraic hierarchy of MV-algebras with product. We connect divisible MV-algebras with \(\mathbb Q\)-vector lattices, we present the divisible hull as a categorical adjunction, and we prove a duality between finitely presented algebras and rational polyhedra.

Keywords

DMV-algebras MV-algebras Rational Łukasiewicz logic Divisible hull Rational polyhedra 

Notes

Acknowledgments

S. Lapenta acknowledges partial support from the Italian National Research Project (PRIN2010-11) entitled Metodi logici per il trattamento dellinformazione. I. Leuştean was supported by a Grant of the Romanian National Authority for Scientific Research and Innovation, CNCS-UEFISCDI, project number PN-II-RU-TE-2014-4-0730.

Compliance with ethical standards

Conflict of interest

Both authors declare that they had no conflict of interest in writing this paper.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of SalernoFiscianoItaly
  2. 2.Department of Computer Science, Faculty of Mathematics and Computer ScienceUniversity of BucharestBucharestRomania

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