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Kleene algebras with implication

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Abstract

Inspired by an old construction due to J. Kalman that relates distributive lattices and centered Kleene algebras, in this paper we study an equivalence for certain categories whose objects are algebras with implication \({(H, \bigwedge, \bigvee, \rightarrow, 0,1)}\) which satisfy the following property for every \({a,b,c\, \in\, H}\): if \({a \leq b \rightarrow c}\), then \({a \bigwedge b \leq c}\).

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Authors and Affiliations

  1. Departamento de Matemática, Facultad de Ciencias Exactas, UNLP and CONICET, Casilla de correos 172, La Plata, (1900), Argentina

    José Luis Castiglioni & Hernán Javier San Martín

  2. Departamento de Matemática, Facultad de Ciencias Exactas, UNCPBA and CONICET, Pinto 399, Tandil, (7000), Argentina

    Sergio Arturo Celani

Authors
  1. José Luis Castiglioni
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  2. Sergio Arturo Celani
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  3. Hernán Javier San Martín
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Corresponding author

Correspondence to José Luis Castiglioni.

Additional information

Presented by C. Tsinakis.

This work was supported by grants CONICET PIP 112-201101-00636 and UNLP 11/X667.

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Castiglioni, J.L., Celani, S.A. & San Martín, H.J. Kleene algebras with implication. Algebra Univers. 77, 375–393 (2017). https://doi.org/10.1007/s00012-017-0433-4

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  • DOI: https://doi.org/10.1007/s00012-017-0433-4

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