Оn the congruence lattices of periodic unary algebras

Автор: Popov Vladimir Valеntinovich

Журнал: Математическая физика и компьютерное моделирование @mpcm-jvolsu

Рубрика: Математика

Статья в выпуске: 2 (21), 2014 года.

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The author describes all commutative unary algebras with finite number of unary operations which have distributive lattice of congruences and cyclic elements in every operation. It proves the following result: Теорема 2. Let A = ???, ??1, ??2,..., ????? is a connected commutative unary algebra, ?? ? 1 and ??1, ??2,..., ???? ? 1 - such a natural numbers, that ?????? ?? (??) = ?? for every ?? ? ?? and every ?? ? ??. Then the following condition are equivalent: (1) The lattice of congruence on A has a distributive property. (2) One can find natural numbers ??1, ??2,..., ???? ? 1 and such an unary operation ? on A, that for every ?? = 1, 2,...,?? and every ?? ? ?? it holds ????(??) = ?????(??).

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Unary operation, commutative unary algebra, lattice of congruence, cyclic element, distributive property

Короткий адрес: https://sciup.org/14968957

IDR: 14968957

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