On pseudo residuated skew lattices

Abstract

In this paper, pseudo residuated skew lattices are defined as a non-commutative generalization of residuated skew lattices and their properties are investigated. It is shown that the class of all conormal pseudo residuated skew lattices forms a variety under some conditions. Dense, regular and strong elements are studied in a pseudo residuated skew lattice and the relationships between them are discussed. We define and investigate different classes of pseudo residuated skew lattices and show that any pseudo residuated skew chain with element 0 is local and also, any locally finite pseudo residuated skew lattice is local. It is shown that any strong pseudo residuated skew lattice is good and any locally finite pseudo residuated skew lattice is good under an extra condition too.

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Acknowledgements

The authors are extremely grateful to the referees for giving them many valuable comments and helpful suggestions which help to improve the presentation of this paper.

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Correspondence to A. Borumand Saeid.

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Koohnavard, R., Borumand Saeid, A. On pseudo residuated skew lattices. Bol. Soc. Mat. Mex. 26, 775–794 (2020). https://doi.org/10.1007/s40590-020-00289-w

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Keywords

  • (Local
  • Locally finite
  • Integral
  • good
  • Strong) pseudo residuated skew lattice
  • Normal filter
  • Dense
  • Regular elements

Mathematics Subject Classification

  • 03G10
  • 06A75
  • 06B20
  • 03B75