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Kites and residuated lattices

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Abstract

We investigate a construction of an integral residuated lattice starting from an integral residuated lattice and two sets with an injective mapping from one set into the second one. The resulting algebra has a shape of a Chinese cascade kite, therefore, we call this algebra simply a kite. We describe subdirectly irreducible kites and we classify them. We show that the variety of integral residuated lattices generated by kites is generated by all finite-dimensional kites. In particular, we describe some homomorphisms among kites.

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Acknowledgements

The authors are very indebted to an anonymous referee for his/her careful reading and suggestions which helped us to improve the presentation of the paper.

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Authors and Affiliations

  1. Palacký University Olomouc Faculty of Sciences, tř. 17.listopadu 12, 771 46, Olomouc, Czech Republic

    Michal Botur & Anatolij Dvurečenskij

  2. Mathematical Institute Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovakia

    Anatolij Dvurečenskij

Authors
  1. Michal Botur
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  2. Anatolij Dvurečenskij
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Correspondence to Anatolij Dvurečenskij.

Additional information

Presented by C. Tsinakis.

Both authors gratefully acknowledge the support by GAČR 15-15286S. AD thanks also the grants APVV-16-0073 and VEGA No. 2/0069/16 SAV.

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Botur, M., Dvurečenskij, A. Kites and residuated lattices. Algebra Univers. 79, 83 (2018). https://doi.org/10.1007/s00012-018-0564-2

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  • DOI: https://doi.org/10.1007/s00012-018-0564-2

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