Some non-standard quasivarieties of lattices
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 standardne...
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2023-09-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
| Subjects: | |
| Online Access: | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/584 |
| _version_ | 1797372735272255488 |
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| author | S.M. Lutsak A.O. Basheyeva A.M. Asanbekov O.A. Voronina |
| author_facet | S.M. Lutsak A.O. Basheyeva A.M. Asanbekov O.A. Voronina |
| author_sort | S.M. Lutsak |
| collection | DOAJ |
| description |
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.
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| first_indexed | 2024-03-08T18:39:10Z |
| format | Article |
| id | doaj.art-9e44fa713cf04aa98b3c162077973100 |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-08T18:39:10Z |
| publishDate | 2023-09-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-9e44fa713cf04aa98b3c1620779731002023-12-29T10:18:49ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112023-09-01111310.31489/2023m3/72-80Some non-standard quasivarieties of latticesS.M. LutsakA.O. BasheyevaA.M. AsanbekovO.A. Voronina 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. http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/584latticequasivarietybasis of quasi-identitiesprofinite algebratopological quasivarietyprofinite quasivariety |
| spellingShingle | S.M. Lutsak A.O. Basheyeva A.M. Asanbekov O.A. Voronina Some non-standard quasivarieties of lattices Қарағанды университетінің хабаршысы. Математика сериясы lattice quasivariety basis of quasi-identities profinite algebra topological quasivariety profinite quasivariety |
| title | Some non-standard quasivarieties of lattices |
| title_full | Some non-standard quasivarieties of lattices |
| title_fullStr | Some non-standard quasivarieties of lattices |
| title_full_unstemmed | Some non-standard quasivarieties of lattices |
| title_short | Some non-standard quasivarieties of lattices |
| title_sort | some non standard quasivarieties of lattices |
| topic | lattice quasivariety basis of quasi-identities profinite algebra topological quasivariety profinite quasivariety |
| url | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/584 |
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