Publication details
Representations of relatively free profinite semigroups, irreducibility, and order primitivity
| Authors | |
|---|---|
| Year of publication | 2020 |
| Type | Article in Periodical |
| Magazine / Source | Transactions of the American Mathematical Society |
| MU Faculty or unit | |
| Citation | |
| Web | https://doi.org/10.1090/tran/7951 |
| 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 |
| 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. |
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