DOAJ Open Access 2023

Some non-standard quasivarieties of lattices

S.M. Lutsak A.O. Basheyeva A.M. Asanbekov O.A. Voronina

Abstrak

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.

Topik & Kata Kunci

Analysis Analytic mechanics Probabilities. Mathematical statistics

Penulis (4)

S.M. Lutsak

A.O. Basheyeva

A.M. Asanbekov

O.A. Voronina

Format Sitasi

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Lutsak, S., Basheyeva, A., Asanbekov, A., Voronina, O. (2023). Some non-standard quasivarieties of lattices. https://doi.org/10.31489/2023M3/72-80

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Informasi Jurnal

Tahun Terbit: 2023
Sumber Database: DOAJ
DOI: 10.31489/2023M3/72-80
Akses: Open Access ✓