REPRESENTATIONS OF RELATIVELY FREE PROFINITE SEMIGROUPS, IRREDUCIBILITY, AND ORDER PRIMITIVITY

• Type: Article in International Scientific Journal
• Date: 2020

Authors

Almeida, J (Author) FCUP; Klima, O (Author) Other

Journal

Title: Transactions of the American Mathematical Society

Vol. 373

Pages: 1941-1981

ISSN: 0002-9947

Publisher: American Mathematical Society

Indexing

ISI Web of Knowledge - 4 Citations

Scopus - 4 Citations

Other information

Authenticus ID: P-00R-VWE

DOI: 10.1090/tran/7951

Abstract (EN): 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 41