Publication details
On semidirectly closed pseudovarieties of finite semigroups and monoids
| Authors | |
|---|---|
| Year of publication | 2022 |
| Type | Article in Periodical |
| Magazine / Source | CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES |
| MU Faculty or unit | |
| Citation | |
| Web | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/C97088F30E561DB1FDD6F5A20DC414D5/S0008439521000564a.pdf/on-semidirectly-closed-pseudovarieties-of-finite-semigroups-and-monoids.pdf |
| Doi | http://dx.doi.org/10.4153/S0008439521000564 |
| Keywords | semidirect product of semigroups; semidirectly closed pseudovariety of finite semigroups; local pseudovariety of finite monoids |
| Description | For every pseudovariety V of finite monoids, let LV denote the pseudovariety of all finite semigroups all of whose local submonoids belong to V. In this paper, it is shown that, for every nontrivial semidirectly closed pseudovariety V of finite monoids, the pseudovariety LV of finite semigroups is also semidirectly closed if, and only if, the given pseudovariety V is local in the sense of Tilson. This finding resolves a long-standing open problem posed in the second volume of the classic monograph by Eilenberg. |
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