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Regular elements and Kolmogorov translation in residuated lattices

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Abstract

In this article, we study in detail the regular elements of a bounded, commutative and integral residuated lattice. We introduce the notion of a regular variety and explore its relationship with the Kolmogorov negative translation. In addition, we investigate the corresponding notions in the axiomatic extensions of the Full Lambek Calculus with exchange and weakening.

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Authors and Affiliations

  1. Departamento de Matemática, Universidad Nacional del Sur, 8000, Bahía Blanca, Argentina

    Diego N. Castaño & J. Patricio Díaz Varela

  2. Facultat de Matemàtiques, Universitat de Barcelona, 08007, Barcelona, Spain

    Antoni Torrens

Authors
  1. Diego N. Castaño
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  2. J. Patricio Díaz Varela
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  3. Antoni Torrens
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Corresponding author

Correspondence to J. Patricio Díaz Varela.

Additional information

Presented by C. Tsinakis.

This paper was prepared partly while the first two authors were visiting the University of Barcelona and IIIA-CSIC, Spain, both supported by CONICET and Universidad Nacional del Sur. The third author was partially supported by Grants 2009SGR1433 of D.G.R. of Generalitat de Catalunya and MTM2011-25747 of D.G.I.C.Y.T. of Spain. The authors are also supported by IRSES project MaToMUVI (PIRSES-GA-2009-247584) of the European Union.

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Castaño, D.N., Díaz Varela, J.P. & Torrens, A. Regular elements and Kolmogorov translation in residuated lattices. Algebra Univers. 73, 1–22 (2015). https://doi.org/10.1007/s00012-014-0311-2

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  • DOI: https://doi.org/10.1007/s00012-014-0311-2

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