Some non-standard quasivarieties of lattices

dc.contributor.author	Lutsak, S.M.
dc.contributor.author	Basheyeva, A.O.
dc.contributor.author	Asanbekov, A.M.
dc.contributor.author	Voronina, O.A.
dc.date.accessioned	2024-12-25T06:21:16Z
dc.date.available	2024-12-25T06:21:16Z
dc.date.issued	2023
dc.identifier.issn	2663-5011
dc.identifier.other	DOI 10.31489/2023M3/72-80
dc.identifier.uri	http://rep.enu.kz/handle/enu/20349
dc.description.abstract	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.	ru
dc.language.iso	en	ru
dc.publisher	Bulletin of the Karaganda University. Mathematics Series	ru
dc.subject	lattice	ru
dc.subject	quasivariety	ru
dc.subject	basis of quasi-identities	ru
dc.subject	profinite algebra	ru
dc.subject	topological quasivariety	ru
dc.subject	profinite quasivariety	ru
dc.title	Some non-standard quasivarieties of lattices	ru
dc.type	Article	ru