DOAJ Open Access 2023

On quasi-identities of finite modular lattices. II

A.O. Basheyeva S.M. Lutsak

Abstrak

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.

Topik & Kata Kunci

Analysis Analytic mechanics Probabilities. Mathematical statistics

Penulis (2)

A.O. Basheyeva

S.M. Lutsak

Format Sitasi

APA MLA BibTeX

Basheyeva, A., Lutsak, S. (2023). On quasi-identities of finite modular lattices. II. https://doi.org/10.31489/2023m2/45-52

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Informasi Jurnal

Tahun Terbit: 2023
Sumber Database: DOAJ
DOI: 10.31489/2023m2/45-52
Akses: Open Access ✓