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- Title
On certain lattices of varieties of completely regular semigroups.
- Authors
Petrich, Mario
- Abstract
The class <italic>CR</italic> of completely regular semigroups considered as algebras with binary multiplication and unary operation of inversion forms a variety. Kernel, trace, local and core relations, denoted by <bold>K</bold>, <bold>T</bold>, <bold>L</bold> and <bold>C</bold>, respectively, are quite useful in studying the structure of the lattice <italic>L</italic>(<italic>CR</italic>) of subvarieties of <italic>CR</italic>. They are equivalence relations whose classes are intervals. Their ends are used for defining operators on <italic>L</italic>(<italic>CR</italic>). Starting with a few band varieties, we repeatedly apply operators induced by upper ends of classes of these relations and characterize corresponding classes up to certain variety low in the lattice <italic>L</italic>(<italic>CR</italic>). We consider only varieties whose origin are “central” band varieties, that is those in the middle column of the lattice <italic>L</italic>(<italic>B</italic>) of band varieties. Several diagrams represent the (semi)lattices studied.
- Subjects
SEMIGROUPS (Algebra); UNARY algebras; KERNEL functions; MIRROR images; MATHEMATICS theorems
- Publication
Studia Scientiarum Mathematicarum Hungarica, 2018, Vol 55, Issue 1, p1
- ISSN
0081-6906
- Publication type
Article
- DOI
10.1556/012.2018.55.1.1366