Authors: Šešelja, Branimir
Tepavčević, Andreja 
Affiliations: Computer Science 
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
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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