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Algebra universalis

, 79:83 | Cite as

Kites and residuated lattices

  • Michal Botur
  • Anatolij Dvurečenskij
Article
  • 19 Downloads

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.

Keywords

Residuated lattice Kite algebra Subdirect irreducible kite Classification of kites 

Mathematics Subject Classification

03G10 03B50 

Notes

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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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Palacký University Olomouc Faculty of SciencesOlomoucCzech Republic
  2. 2.Mathematical Institute Slovak Academy of SciencesBratislavaSlovakia

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