Globals of pseudovarieties of commutative semigroups: The finite basis problem, decidability and gaps

• Type: Article in International Scientific Journal
• Date: 2001

Authors

Almeida, J (Author) FCUP; Azevedo, A (Author) Other

Journal

Title: Proceedings of the Edinburgh Mathematical Society

Vol. 44

Pages: 27-47

ISSN: 0013-0915

Publisher: Cambridge University Press

Indexing

ISI Web of Knowledge - 7 Citations

Scopus - 6 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-000-WJX

DOI: 10.1017/s0013091599000486

Abstract (EN): Whereas pseudovarieties of commutative semigroups are known to be finitely based, the globals of monoidal pseudovarieties of commutative semigroups are shown to be finitely based (or of finite vertex rank) if and only if the index is 0, 1 or omega. Nevertheless, on these pseudovarieties, the operation of taking the global preserves decidability Furthermore, the gaps between many of these globals are shown to be big in the sense that they contain chains which are order isomorphic to the reals.

Language: English

Type (Professor's evaluation): Scientific