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@article{1696309,
author = {Almeida, Jorge and Klíma, Ondřej},
article_location = {Providence},
article_number = {3},
doi = {http://dx.doi.org/10.1090/tran/7951},
keywords = {Pseudovariety; relatively free profinite semigroup; torsion; group mapping semigroup; minimum ideal; join irreducibility; ordered semigroup},
language = {eng},
issn = {0002-9947},
journal = {Transactions of the American Mathematical Society},
title = {Representations of relatively free profinite semigroups, irreducibility, and order primitivity},
url = {https://doi.org/10.1090/tran/7951},
volume = {373},
year = {2020}
}
TY - JOUR
ID - 1696309
AU - Almeida, Jorge - Klíma, Ondřej
PY - 2020
TI - Representations of relatively free profinite semigroups, irreducibility, and order primitivity
JF - Transactions of the American Mathematical Society
VL - 373
IS - 3
SP - 1941-1981
EP - 1941-1981
PB - American Mathematical Society
SN - 00029947
KW - Pseudovariety
KW - relatively free profinite semigroup
KW - torsion
KW - group mapping semigroup
KW - minimum ideal
KW - join irreducibility
KW - ordered semigroup
UR - https://doi.org/10.1090/tran/7951
L2 - https://doi.org/10.1090/tran/7951
N2 - We establish that, under certain closure assumptions on a pseudovariety of semigroups, the corresponding relatively free profinite semigroups freely generated by a nonsingleton finite set act faithfully on their minimum ideals. As applications, we enlarge the scope of several previous join irreducibility results for pseudovarieties of semigroups, which turn out to be even join irreducible in the lattice of pseudovarieties of ordered semigroups, so that, in particular, they are not generated by proper subpseudovarieties of ordered semigroups. We also prove the stronger form of join irreducibility for the Krohn-Rhodes complexity pseudovarieties, thereby solving a problem proposed by Rhodes and Steinberg.
ER -
ALMEIDA, Jorge and Ondřej KLÍMA. Representations of relatively free profinite semigroups, irreducibility, and order primitivity. \textit{Transactions of the American Mathematical Society}. Providence: American Mathematical Society, 2020, vol.~373, No~3, p.~1941-1981. ISSN~0002-9947. Available from: https://dx.doi.org/10.1090/tran/7951.
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