Geodesic
A semilattice of varieties of completely regular semigroups
Mathematica Bohemica, Tome 145 (2020) no. 1, pp. 1-14.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Completely regular semigroups are unions of their (maximal) subgroups with the unary operation within their maximal subgroups. As such they form a variety whose lattice of subvarieties is denoted by $\mathcal L(\mathcal C\mathcal R)$. \endgraf We construct a 60-element $\cap $-subsemilattice and a 38-element sublattice of $\mathcal L(\mathcal C\mathcal R)$. The bulk of the paper consists in establishing the necessary joins for which it uses Polák's theorem.
DOI : 10.21136/MB.2018.0112-17
Classification : 20M07
Keywords: completely regular semigroup; lattice; variety; $\cap $-subsemilattice 
@article{10_21136_MB_2018_0112_17,
     author = {Petrich, Mario},
     title = {A semilattice of varieties of completely regular semigroups},
     journal = {Mathematica Bohemica},
     pages = {1--14},
     publisher = {mathdoc},
     volume = {145},
     number = {1},
     year = {2020},
     doi = {10.21136/MB.2018.0112-17},
     mrnumber = {4088688},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2018.0112-17/}
}
TY  - JOUR
AU  - Petrich, Mario
TI  - A semilattice of varieties of completely regular semigroups
JO  - Mathematica Bohemica
PY  - 2020
SP  - 1
EP  - 14
VL  - 145
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2018.0112-17/
DO  - 10.21136/MB.2018.0112-17
LA  - en
ID  - 10_21136_MB_2018_0112_17
ER  - 
%0 Journal Article
%A Petrich, Mario
%T A semilattice of varieties of completely regular semigroups
%J Mathematica Bohemica
%D 2020
%P 1-14
%V 145
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2018.0112-17/
%R 10.21136/MB.2018.0112-17
%G en
%F 10_21136_MB_2018_0112_17
Petrich, Mario. A semilattice of varieties of completely regular semigroups. Mathematica Bohemica, Tome 145 (2020) no. 1, pp. 1-14. doi : 10.21136/MB.2018.0112-17. http://geodesic.mathdoc.fr/articles/10.21136/MB.2018.0112-17/

Cité par Sources :