Endomorphisms of the lattice of epigroup varieties
| Autor: | Gusev, S. V., Vernikov, B. M. |
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| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | Semigroup Forum 93 (2016), 554-574 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00233-016-9825-6 |
| Popis: | We examine varieties of epigroups as unary semigroups, that is semigroups equipped with an additional unary operation of pseudoinversion. The article contains two main results. The first of them indicates a countably infinite family of injective endomorphisms of the lattice of all epigroup varieties. An epigroup variety is said to be a variety of finite degree if all its nilsemigroups are nilpotent. The second result of the article provides a characterization of epigroup varieties of finite degree in a language of identities and in terms of minimal forbidden subvarieties. Note that the first result is essentially used in the proof of the second one. Comment: In comparison with the previous version, we eliminate a few typos only |
| Databáze: | arXiv |
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