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Title: | Construction of a complementary quasiorder |
Authors: | Jakubíková -Studenovská, D. Janičková, L. |
Keywords: | monounary algebra quasiorder lattice complement complemented lattice. |
Issue Date: | 2018 |
Publisher: | ДЗ "ЛНУ імені Тараса Шевченка" |
Series/Report no.: | Математичні науки; |
Abstract: | For a monounary algebra A = (A, f) we study the lattice Quord A of all quasiorders of A, i.e., of all reflexive and transitive relations compatible with f. Monounary algebras (A, f) whose lattices of quasiorders are complemented were characterized in 2011 as follows: (∗) f(x) is a cyclic element for all x ∈ A, and all cycles have the same square-free number n of elements. Sufficiency of the condition (∗) was proved by means of transfinite induction. Now we will describe a construction of a complement to a given quasiorder of (A, f) satisfying (∗). |
Description: | Jakubíková -Studenovská D. Construction of a complementary quasiorder / D. Jakubíková -Studenovská , L. Janičková // Algebra and Discrete Mathematics. - 2019. - Vol. 27. - Number 1. - Рp. 39 -55 |
URI: | http://hdl.handle.net/123456789/4485 |
Appears in Collections: | Algebra and Discrete Mathematics. - № 1 (25). - 2018 |
Files in This Item:
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335-3175-1-PB.pdf | 440.45 kB | Adobe PDF | View/Open |
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