Geodesic
On join irreducible J-trivial semigroups
Rendiconti del Seminario Matematico della Università di Padova, Tome 147 (2022), pp. 43-78

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

DOI MR   Zbl

A pseudovariety of semigroups is join irreducible if, whenever it is contained in the complete join of some pseudovarieties, then it is contained in one of the pseudovarieties. A finite semigroup is join irreducible if it generates a join irreducible pseudovariety. New finite 𝒥-trivial semigroups 𝒞 n (n≥2) are exhibited with the property that, while each 𝒞 n is not join irreducible, the monoid 𝒞 n I is join irreducible. The monoids 𝒞 n I are the first examples of join irreducible 𝒥-trivial semigroups that generate pseudovarieties that are not self-dual. Several sufficient conditions are also established under which a finite semigroup is not join irreducible. Based on these results, join irreducible pseudovarieties generated by a 𝒥-trivial semigroup of order up to six are completely described. It turns out that besides known examples and those generated by 𝒞 2 I and its dual monoid, there are no further examples.

Accepté le :
Publié le :
DOI : 10.4171/rsmup/90
Classification : 20, 08 
Lee, Edmond W.  H.; Rhodes, John; Steinberg, Benjamin. On join irreducible $J$-trivial semigroups. Rendiconti del Seminario Matematico della Università di Padova, Tome 147 (2022), pp. 43-78. doi: 10.4171/rsmup/90
@article{RSMUP_2022__147__43_0,
     author = {Lee, Edmond W. \hspace{1pt}H. and Rhodes, John and Steinberg, Benjamin},
     title = {On join irreducible $J$-trivial semigroups},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {43--78},
     year = {2022},
     volume = {147},
     doi = {10.4171/rsmup/90},
     mrnumber = {4450783},
     zbl = {1506.20089},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/rsmup/90/}
}
TY  - JOUR
AU  - Lee, Edmond W.  H.
AU  - Rhodes, John
AU  - Steinberg, Benjamin
TI  - On join irreducible $J$-trivial semigroups
JO  - Rendiconti del Seminario Matematico della Università di Padova
PY  - 2022
SP  - 43
EP  - 78
VL  - 147
UR  - http://geodesic.mathdoc.fr/articles/10.4171/rsmup/90/
DO  - 10.4171/rsmup/90
LA  - en
ID  - RSMUP_2022__147__43_0
ER  - 
%0 Journal Article
%A Lee, Edmond W.  H.
%A Rhodes, John
%A Steinberg, Benjamin
%T On join irreducible $J$-trivial semigroups
%J Rendiconti del Seminario Matematico della Università di Padova
%D 2022
%P 43-78
%V 147
%U http://geodesic.mathdoc.fr/articles/10.4171/rsmup/90/
%R 10.4171/rsmup/90
%G en
%F RSMUP_2022__147__43_0

Cité par Sources :