A conjecture for varieties of completely regular semigroups
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Mario Petrich
Abstract
The class 𝒞ℛ of completely regular semigroups considered with the unary operation of inversion within maximal subgroups forms a variety. The B-relation on the lattice ℒ(𝒞ℛ) of subvarieties of 𝒞ℛ identifies two varieties if they contain the same bands. Its classes are intervals with the set Δ of upper ends of these intervals. Canonical varieties form part of Δ. Previously we determined the sublattice Ψ of ℒ(𝒞ℛ) generated by the variety 𝒞𝒮 of completely simple semigroups and six canonical varieties.
The conjecture is that the sublattice of ℒ(𝒞ℛ) generated by 𝒞𝒮 and canonical varieties follows the pattern of the structure of Ψ.
(Communicated by Vincenzo Marra )
Acknowledgement
Assistance by Edmond W. H. Lee is deeply appreciated.
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© 2019 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- Regular papers
- The life jubilee of Prof. RNDr. Sylvia Pulmannová, DrSc.
- Perfect 1-factorizations
- A topological duality for strong Boolean posets
- On the Diophantine equations x2 + 2α 3β 19γ = yn and x2 + 2α 3β 13γ = yn
- Tribonacci numbers and primes of the form p = x2 + 11y2
- Basic semirings
- A conjecture for varieties of completely regular semigroups
- Uniqueness of meromorphic function with its shift operator under the purview of two or three shared sets
- Differential subordination results for Mittag-Leffler type functions with bounded turning property
- Mittag-Leffler stability for non-instantaneous impulsive Caputo fractional differential equations with delays
- Asymptotically periodic behavior of solutions of fractional evolution equations of order 1 < α < 2
- On the polynomial entropy for morse gradient systems
- Quantitative approximation by Stancu-Durrmeyer-Choquet-Šipoš operators
- A note on non-linear ∗-Jordan derivations on ∗-algebras
- Disjoint hypercyclic weighted translations on locally compact hausdorff spaces
- Some new results on real hypersurfaces with generalized Tanaka-Webster connection
- Relative topological properties of hyperspaces
- Cohomology of torus manifold bundles
- The Menger and projective Menger properties of function spaces with the set-open topology
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