Mathematical Institute of the Serbian Academy of Sciences and Arts
|Title:||Congruences on Lattices and Lattice-Valued Functions||Journal:||Computational Intelligence and Mathematics for Tackling Complex Problems 2||Series/Report no.:||Studies in Computational Intelligence||Volume:||955||First page:||219||Last page:||228||Conference:||11th European Symposium on Computational Intelligence and Mathematics, ESCIM 2019||Issue Date:||1-Jan-2022||Rank:||M33||ISBN:||9783030888169||ISSN:||1860-949X||DOI:||10.1007/978-3-030-88817-6_25||Abstract:||
For a complete lattice L and an L-valued function μ on a domain X, the cuts of μ determine a residuated map f from L to the power set of X ordered dually to inclusion. We describe a class of complete lattices for which the kernel of f is a complete congruence on L. Conversely, every complete congruence on a complete lattice L is uniquely determined by a suitable L-valued function μ on an arbitrary domain, as the kernel of a residuated map which sends every element p∈ L into the corresponding cut μp. As an application, using residuated maps we get a representation of finite lattices by meet-irreducible elements.
|Keywords:||Closure operators | Cuts | L-valued functions | Residuated maps||Publisher:||Springer Link||Project:||Development of methods of computation and information processing: theory and applications|
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