Some non-standard quasivarieties of lattices
Кейбiр стандартты емес торлардың квазикөпбейнелерi
Некоторые нестандартные квазимногообразия решеток
Lutsak S.M. Basheyeva A.O. Asanbekov A.M. Voronina O.A.
2023E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2023#111Issue 372 - 80 pp.
The questions of the standardness of quasivarieties have been investigated by many authors. The problem Which finite lattices generate a standard topological prevariety? was suggested by D.M. Clark, B.A. Davey, M.G. Jackson and J.G. Pitkethly in 2008. We continue to study the standardness problem for one specific finite modular lattice which does not satisfy all Tumanov’s conditions. We investigate the topological quasivariety generated by this lattice and we prove that the researched quasivariety is not standard, as well as is not finitely axiomatizable. We also show that there is an infinite number of lattices similar to the lattice mentioned above.
basis of quasi-identities , lattice , profinite algebra , profinite quasivariety , quasivariety , topological quasivariety
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M. Kozybayev North Kazakhstan University, Petropavlovsk, Kazakhstan
L.N. Gumilyov Eurasian National University, Astana, Kazakhstan
Institute of Mathematics, NAS KR, Bishkek, Kyrgyzstan
M. Kozybayev North Kazakhstan University
L.N. Gumilyov Eurasian National University
Institute of Mathematics
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