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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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