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Soft Computing

, Volume 22, Issue 22, pp 7519–7537 | Cite as

Morphisms on \({ EMV}\)-algebras and their applications

  • Anatolij Dvurečenskij
  • Omid Zahiri
Foundations
  • 66 Downloads

Abstract

For a new class of algebras, called \({ EMV}\)-algebras, every idempotent element a determines an \({ MV}\)-algebra which is important for the structure of the \({ EMV}\)-algebra. Therefore, instead of standard homomorphisms of \({ EMV}\)-algebras, we introduce \({ EMV}\)-morphisms as a family of \({ MV}\)-homomorphisms from \({ MV}\)-algebras [0, a] into other ones. \({ EMV}\)-morphisms enable us to study categories of \({ EMV}\)-algebras where objects are \({ EMV}\)-algebras and morphisms are special classes of \({ EMV}\)-morphisms. The category is closed under product. In addition, we define free \({ EMV}\)-algebras on a set X with respect to \({ EMV}\)-morphisms. If X is finite, then a free \({ EMV}\)-algebra on X is termwise equivalent to the free \({ MV}\)-algebra on X. For an infinite set X, the same is true introducing a so-called weakly free \({ EMV}\)-algebra.

Keywords

\({ MV}\)-algebra \({ EMV}\)-algebra \({ EMV}\)-homomorphism \({ EMV}\)-morphism Standard \({ EMV}\)-morphism Free \({ EMV}\)-algebra Weakly free \({ EMV}\)-algebra Categories of \({ EMV}\)-algebras 

Notes

Acknowledgements

AD is thankful for the support by the Slovak Research and Development Agency under the Contract No. APVV-16-0073 and by Grants VEGA No. 2/0069/16 SAV and GAČR 15-15286S.

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest.

Human participants

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 GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mathematical InstituteSlovak Academy of SciencesBratislavaSlovakia
  2. 2.Depart. Algebra Geom.Palacký Univer.OlomoucCzech Republic
  3. 3.University of Applied Science and TechnologyTehranIran

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