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|Title:||Cancellable Elements of the Lattice of Monoid Varieties|
|Authors:||Gusev, S. V.|
Lee, E. W. H.
|Publisher:||Springer Science and Business Media B.V.|
Springer Science and Business Media LLC
|Citation:||Gusev S. V. Cancellable Elements of the Lattice of Monoid Varieties / S. V. Gusev, E. W. H. Lee. — DOI 10.3390/plants11060762 // Acta Mathematica Hungarica. — 2021. — Vol. 165. — Iss. 1. — P. 156-168.|
|Abstract:||The set of all cancellable elements of the lattice of semigroup varieties has recently been shown to be countably infinite. But the description of all cancellable elements of the lattice MON of monoid varieties remains unknown. This problem is addressed in the present article. The first example of a monoid variety with modular but non-distributive subvariety lattice is first exhibited. Then a necessary condition of the modularity of an element in MON is established. These results play a crucial role in the complete description of all cancellable elements of the lattice MON. It turns out that there are precisely five such elements. © 2021, Akadémiai Kiadó, Budapest, Hungary.|
|Keywords:||CANCELLABLE ELEMENT OF A LATTICE|
LATTICE OF VARIETIES
MODULAR ELEMENT OF A LATTICE
|metadata.dc.description.sponsorship:||The first author is supported by the Ministry of Science and Higher Education of the Russian Federation (project FEUZ-2020-0016).|
|Appears in Collections:||Научные публикации, проиндексированные в SCOPUS и WoS CC|
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