Representations of relatively free profinite semigroups, irreducibility, and order primitivity

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F20%3A00114486" target="_blank" >RIV/00216224:14310/20:00114486 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1090/tran/7951" target="_blank" >https://doi.org/10.1090/tran/7951</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/tran/7951" target="_blank" >10.1090/tran/7951</a>

Result language
angličtina
Original language name
Representations of relatively free profinite semigroups, irreducibility, and order primitivity
Original language description
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.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA15-02862S" target="_blank" >GA15-02862S: Applications of Algebra and Combinatorics in Formal Language Theory</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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