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Algebra universalis

, Volume 77, Issue 4, pp 375–393 | Cite as

Kleene algebras with implication

  • José Luis CastiglioniEmail author
  • Sergio Arturo Celani
  • Hernán Javier San Martín
Article

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 \({a \bigwedge b \leq c}\).

Key words and phrases

involutive distributive lattices centered Kleene algebras lattices with implication 

2010 Mathematics Subject Classification

Primary: 06D99 Secondary: 06D05 08A30 08A62 

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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  • José Luis Castiglioni
    • 1
    Email author
  • Sergio Arturo Celani
    • 2
  • Hernán Javier San Martín
    • 1
  1. 1.Departamento de Matemática, Facultad de Ciencias ExactasUNLP and CONICETLa PlataArgentina
  2. 2.Departamento de Matemática, Facultad de Ciencias ExactasUNCPBA and CONICETTandilArgentina

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