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

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

Journal

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

Output data

Year: 2024, Volume: 63, Number: 2, Pages: 114-140 Pages count : 27 DOI: 10.1007/s10469-025-09776-3

Funding (2)

1	Sobolev Institute of Mathematics	FWNF-2022-0012
2	Russian Science Foundation	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

Submitted:	Apr 30, 2023
Accepted:	Dec 6, 2024
Published print:	Jan 31, 2025
Published online:	Jan 31, 2025

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

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