On quasi-identities of finite modular lattices. II
Соңғы модулярлық торлардың квазитепе-теңдiктерi туралы. II
О квазитождествах конечных модулярных решеток. II
Basheyeva A.O. Lutsak S.M.
2023E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2023#110Issue 245 - 52 pp.
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 quasi-identity 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.
finite basis of quasi-identities , finite lattice , identity , lattice , modular lattice , quasi-identity , quasivariety , Tumanov’s conditions , variety
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L.N. Gumilyov Eurasian National University, Astana, Kazakhstan
M. Kozybayev North Kazakhstan University, Petropavlovsk, Kazakhstan
L.N. Gumilyov Eurasian National University
M. Kozybayev North Kazakhstan University
10 лет помогаем публиковать статьи Международный издатель
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