On quasi-identities of finite modular lattices. II

dc.contributor.author	Basheyeva, A.O.
dc.contributor.author	Lutsak, S.M.
dc.date.accessioned	2024-12-18T07:28:56Z
dc.date.available	2024-12-18T07:28:56Z
dc.date.issued	2023
dc.identifier.issn	2663-5011
dc.identifier.other	DOI 10.31489/2023M2/45-52
dc.identifier.uri	http://rep.enu.kz/handle/enu/20324
dc.description.abstract	The existence of a finite identity basis for any finite lattice was established by R. McKenzie in 1970, but the analogous statement for quasi-identities is incorrect. So, there is a finite lattice that does not have a finite quasi-identity basis and, V.A. Gorbunov and D.M. Smirnov asked which finite lattices have finite quasiidentity bases. In 1984 V.I. Tumanov conjectured that a proper quasivariety generated by a finite modular lattice is not finitely based. He also found two conditions for quasivarieties which provide this conjecture. We construct a finite modular lattice that does not satisfy Tumanov’s conditions but quasivariety generated by this lattice is not finitely based.	ru
dc.language.iso	en	ru
dc.publisher	Bulletin of the Karaganda University. Mathematics Series	ru
dc.relation.ispartofseries	№ 2(110)/2023;
dc.subject	lattice	ru
dc.subject	finite lattice	ru
dc.subject	modular lattice	ru
dc.subject	modular lattice	ru
dc.subject	quasivariety	ru
dc.subject	variety	ru
dc.subject	quasi-identity	ru
dc.subject	identity	ru
dc.subject	finite basis of quasi-identities	ru
dc.subject	Tumanov’s conditions	ru
dc.title	On quasi-identities of finite modular lattices. II	ru
dc.type	Article	ru

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