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Soft Computing

, Volume 22, Issue 22, pp 7505–7517 | Cite as

Involutive equality algebras

  • R. A. Borzooei
  • M. Zarean
  • O. Zahiri
Foundations

Abstract

The present paper aims to study a special class of equality algebras, called involutive equality algebra. We obtain some properties of this structure and prove that every linearly ordered 0-compatible equality algebra includes a \((\sim _0)\)-involutive subalgebra. We prove that each \((\sim _0)\)-involutive equality algebra is a lattice, while it is distributive under a suitable condition. Then, we define \((\sim _0)\)-involutive deductive systems on bounded equality algebras and represent a condition under which the set of all dense elements of an equality algebra is a \((\sim _0)\)-involutive deductive system. Finally, we find the relations among 0-compatible equality algebras, residuated lattices and Boolean algebras.

Keywords

Equality algebra Involutive equality algebra Residuated lattice Boolean algebra 

Mathematics Subject Classification

03G25 06F05 06F35 

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest.

Human and animal rights

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.Department of MathematicsShahid Beheshti UniversityTehranIran
  2. 2.Department of MathematicsPayame Noor UniversityTehranIran
  3. 3.University of Applied Science and TechnologyTehranIran

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