Наукова електронна бібліотека
періодичних видань НАН України
періодичних видань НАН України
Construction of a complementary quasiorder
Репозиторій DSpace/Manakin
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Construction of a complementary quasiorder
Інший ID:
2010 MSC: 08A60, 08A02.
Посилання:
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.
Підтримка:
This work was supported by Grant VEGA 1/0063/14 and VEGA 1/0097/18.
Дата:
2018
Переглядів:
172
Завантажень:
68
Анотація:
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 (*).
