Duality for Bi-Algebraic Lattices Belonging to the Variety of (0, 1)-Lattices Generated by the Pentagon | Sciact - Система учета научной деятельности ИМ СО РАН

Duality for Bi-Algebraic Lattices Belonging to the Variety of (0, 1)-Lattices Generated by the Pentagon Научная публикация

Журнал

Algebra and Logic
ISSN: 0002-5232 , E-ISSN: 1573-8302

Вых. Данные

Год: 2024, Том: 63, Номер: 2, Страницы: 114-140 Страниц : 27 DOI: 10.1007/s10469-025-09776-3

Ключевые слова

duality, bi-algebraic lattice, variety

Авторы

Dziobiak W. ¹ , Schwidefsky M.V. ^2,3

Организации

1	Department of Mathematical Sciences, University of Puerto Rico, Mayag¨uez, PR 00681, USA;
2	Novosibirsk State University, Novosibirsk, Russia
3	Sobolev Institute of Mathematics, Novosibirsk, Russia

Информация о финансировании (2)

1	Институт математики им. С.Л. Соболева СО РАН	FWNF-2022-0012
2	Российский научный фонд	22-21-00104

According to G. Birkhoff, there is a categorical duality between the category of bi-algebraic distributive (0,1)-lattices with complete (0,1)-lattice homomorphisms as morphisms and the category of partially ordered sets with partial order-preserving maps as morphisms. We extend this classical result to the bi-algebraic lattices belonging to the variety of (0,1)-lattices generated by the pentagon, the 5-element nonmodular lattice. Applying the extended duality, we prove that the lattice of quasivarieties contained in the variety of (0,1)-lattices generated by the pentagon has uncountably many elements and is not distributive. This yields the following: the lattice of quasivarieties contained in a nontrivial variety of (0,1)-lattices either is a 2-element chain or has uncountably many elements and is not distributive.

Dziobiak W. , Schwidefsky M.V.
Duality for Bi-Algebraic Lattices Belonging to the Variety of (0, 1)-Lattices Generated by the Pentagon
Algebra and Logic. 2024. V.63. N2. P.114-140. DOI: 10.1007/s10469-025-09776-3 WOS РИНЦ OpenAlex

Дзебяк В. , Швидефски М.В.
Дуальность для биалгебраических решёток, принадлежащих многообразию (0,1)-решёток, порождённому пентагоном
Алгебра и логика. 2024. Т.63. №2. С.167-208. DOI: 10.33048/alglog.2024.63.204 РИНЦ

Поступила в редакцию:	30 апр. 2023 г.
Принята к публикации:	6 дек. 2024 г.
Опубликована в печати:	31 янв. 2025 г.
Опубликована online:	31 янв. 2025 г.

Web of science:	WOS:001410158100001
РИНЦ:	81349191
OpenAlex:	W4407051227

Пока нет цитирований