Semi-lattice of varieties of quasigroups with linearity
A σ-parastrophe of a class of quasigroups 𝕬 is a class σ𝕬 of all σ-parastrophes of quasigroups from 𝕬. A set of all pairwise parastrophic classes is called a parastrophic orbit or a truss. A parastrophically closed semi-lattice of classes is a bunch. A linearity bunch is a set of varieties which con...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2021 |
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Інститут прикладної математики і механіки НАН України
2021
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| Zitieren: | Semi-lattice of varieties of quasigroups with linearity / F.M. Sokhatsky, H.V. Krainichuk, V.A. Sydoruk // Algebra and Discrete Mathematics. — 2021. — Vol. 31, № 2. — С. 261–285. — Бібліогр.: 29 назв. — англ. |
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Sokhatsky, F.M. Krainichuk, H.V. Sydoruk, V.A. 2023-03-11T16:15:09Z 2023-03-11T16:15:09Z 2021 Semi-lattice of varieties of quasigroups with linearity / F.M. Sokhatsky, H.V. Krainichuk, V.A. Sydoruk // Algebra and Discrete Mathematics. — 2021. — Vol. 31, № 2. — С. 261–285. — Бібліогр.: 29 назв. — англ. 1726-3255 DOI:10.12958/adm1748 2020 MSC: Primary 20N05, 20N15, 39B52, 08A05; Secondary 05A15, 05B07 https://nasplib.isofts.kiev.ua/handle/123456789/188711 A σ-parastrophe of a class of quasigroups 𝕬 is a class σ𝕬 of all σ-parastrophes of quasigroups from 𝕬. A set of all pairwise parastrophic classes is called a parastrophic orbit or a truss. A parastrophically closed semi-lattice of classes is a bunch. A linearity bunch is a set of varieties which contains the variety of all left linear quasigroups, the variety of all left alinear quasi-groups, all their parastrophes and all their intersections. It contains 14 varieties, which are distributed into six parastrophic orbits. All quasigroups from these varieties are called dilinear. To obtain all varieties from the bunch, concepts of middle linearity and middle alinearity are introduced. A well-known identity or a system of identities which describes a variety from every parastrophic orbit of the bunch is cited. An algorithm for obtaining identities which describe all varieties from the parastrophic orbits is given. Examples of quasigroups distinguishing one variety from the other are presented. The authors are grateful to the members of Scientific Ukrainian Mathematical School “Multiary Invertible Functions” (SUMS “MIF”) for their helpful discussions on the problem and to the English reviewer V. Obshanska. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Semi-lattice of varieties of quasigroups with linearity Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Semi-lattice of varieties of quasigroups with linearity |
| spellingShingle |
Semi-lattice of varieties of quasigroups with linearity Sokhatsky, F.M. Krainichuk, H.V. Sydoruk, V.A. |
| title_short |
Semi-lattice of varieties of quasigroups with linearity |
| title_full |
Semi-lattice of varieties of quasigroups with linearity |
| title_fullStr |
Semi-lattice of varieties of quasigroups with linearity |
| title_full_unstemmed |
Semi-lattice of varieties of quasigroups with linearity |
| title_sort |
semi-lattice of varieties of quasigroups with linearity |
| author |
Sokhatsky, F.M. Krainichuk, H.V. Sydoruk, V.A. |
| author_facet |
Sokhatsky, F.M. Krainichuk, H.V. Sydoruk, V.A. |
| publishDate |
2021 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| description |
A σ-parastrophe of a class of quasigroups 𝕬 is a class σ𝕬 of all σ-parastrophes of quasigroups from 𝕬. A set of all pairwise parastrophic classes is called a parastrophic orbit or a truss. A parastrophically closed semi-lattice of classes is a bunch. A linearity bunch is a set of varieties which contains the variety of all left linear quasigroups, the variety of all left alinear quasi-groups, all their parastrophes and all their intersections. It contains 14 varieties, which are distributed into six parastrophic orbits. All quasigroups from these varieties are called dilinear. To obtain all varieties from the bunch, concepts of middle linearity and middle alinearity are introduced. A well-known identity or a system of identities which describes a variety from every parastrophic orbit of the bunch is cited. An algorithm for obtaining identities which describe all varieties from the parastrophic orbits is given. Examples of quasigroups distinguishing one variety from the other are presented.
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| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/188711 |
| citation_txt |
Semi-lattice of varieties of quasigroups with linearity / F.M. Sokhatsky, H.V. Krainichuk, V.A. Sydoruk // Algebra and Discrete Mathematics. — 2021. — Vol. 31, № 2. — С. 261–285. — Бібліогр.: 29 назв. — англ. |
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2025-12-07T18:01:45Z |
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2025-12-07T18:01:45Z |
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