Geodesic
On semidirectly closed pseudovarieties of finite semigroups and monoids
Canadian mathematical bulletin, Tome 65 (2022) no. 3, pp. 612-627

Voir la notice de l'article provenant de la source Cambridge

DOI

For every pseudovariety $\mathbf {V}$ of finite monoids, let $\mathbf {LV}$ denote the pseudovariety of all finite semigroups all of whose local submonoids belong to $\mathbf {V}$. In this paper, it is shown that, for every nontrivial semidirectly closed pseudovariety $\mathbf {V}$ of finite monoids, the pseudovariety $\mathbf {LV}$ of finite semigroups is also semidirectly closed if, and only if, the given pseudovariety $\mathbf {V}$ 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.
DOI : 10.4153/S0008439521000564
Mots-clés : semidirect product of semigroups, semidirectly closed pseudovariety of finite semigroups, local pseudovariety of finite monoids 
Kad’ourek, Jiří. On semidirectly closed pseudovarieties of finite semigroups and monoids. Canadian mathematical bulletin, Tome 65 (2022) no. 3, pp. 612-627. doi: 10.4153/S0008439521000564
@article{10_4153_S0008439521000564,
     author = {Kad{\textquoteright}ourek, Ji\v{r}{\'\i}},
     title = {On semidirectly closed pseudovarieties of finite semigroups and monoids},
     journal = {Canadian mathematical bulletin},
     pages = {612--627},
     year = {2022},
     volume = {65},
     number = {3},
     doi = {10.4153/S0008439521000564},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439521000564/}
}
TY  - JOUR
AU  - Kad’ourek, Jiří
TI  - On semidirectly closed pseudovarieties of finite semigroups and monoids
JO  - Canadian mathematical bulletin
PY  - 2022
SP  - 612
EP  - 627
VL  - 65
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/S0008439521000564/
DO  - 10.4153/S0008439521000564
ID  - 10_4153_S0008439521000564
ER  - 
%0 Journal Article
%A Kad’ourek, Jiří
%T On semidirectly closed pseudovarieties of finite semigroups and monoids
%J Canadian mathematical bulletin
%D 2022
%P 612-627
%V 65
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/S0008439521000564/
%R 10.4153/S0008439521000564
%F 10_4153_S0008439521000564

Cité par Sources :