Construction of a complementary quasiorder
For a monounary algebra A = (A, f) we study the lattice QuordA 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...
Збережено в:
| Дата: | 2018 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2018
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/188347 |
| Теги: |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Construction of a complementary quasiorder / D. Jakubíková-Studenovská, L. Janičková // Algebra and Discrete Mathematics. — 2018. — Vol. 25, № 1. — С. 39-55. — Бібліогр.: 4 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | For a monounary algebra A = (A, f) we study the lattice QuordA 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 (*). |
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