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.
