The quasivariety SP (M3). II. Duality
https://doi.org/10.26907/2949-3919.2026.1.67-91
Abstract
The diamond M3 is a five-element lattice which is the smallest nondistributive modular lattice. We establish the dual equivalence of the category with objects being bi-algebraic lattices belonging to the variety generated by M3 and with morphisms being complete lattice homomorphisms and the category with objects, called by us M3-spaces, being ordered spaces endowed with an equivalence relation and with so-called M3-morphisms. A similar result for the pentagon N5, a five-element lattice which is the smallest non-modular lattice, was established earlier by W. Dziobiak and the second author. The so-called N5-spaces there and M3-spaces here are completely different. However, morphisms between N5-spaces and between M3-spaces, respectively, are an application of an old concept – the minimal join cover refinement property for join covers of an element in a lattice.
Supporting agencies: The work is supported by the Russian Science Foundation (project № 24-21-00075), https://rscf.ru/project/24-21-00075/
About the Authors
A. E. Izyurova
Novosibirsk State University
Russian Federation
Russian Federation
Aleksandra Evgenyevna Izyurova
1 Pirogov str., Novosibirsk 630090
M. V. Schwidefsky
Novosibirsk State University; Sobolev Institute of Mathematics SB RAS
Russian Federation
Russian Federation
Marina Vladimirovna Schwidefsky
1 Pirogov str., Novosibirsk 630090; 4 Acad. Koptyug Ave., Novosibirsk 630090
References
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Review
For citations:
Izyurova A.E., Schwidefsky M.V. The quasivariety SP (M3). II. Duality. Mathematics and Theoretical Computer Science. 2026;4(1):67-91. (In Russ.) https://doi.org/10.26907/2949-3919.2026.1.67-91
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