On finitely based pseudovarieties of the forms V*D and V*D-n

• Type: Article in International Scientific Journal
• Date: 2000

Authors

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

Journal

Title: Journal of Pure and Applied Algebra

Vol. 146

Pages: 1-15

ISSN: 0022-4049

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 14 Citations

Scopus - 14 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-001-0TX

DOI: 10.1016/s0022-4049(98)00162-5

Abstract (EN): Let D-n be the pseudovariety of all finite semigroups in which products of length n are right zeros and let D = boolean ORn>1 D-n. It is shown in this paper that, if V is a pseudovariety of semi groups whose global g (V) over bar is finitely based, then V (*) D-n (n greater than or equal to 1) and V (*) D are also finitely based. Moreover, if V is itself finitely based and contains the aperiodic five-element Brandt semigroup, then gV is also finitely based. As a further application, it is proved that the finite basis properties for gV, V (*) D and V (*) D-n (n greater than or equal to 1) are all equivalent for an arbitrary non-group monoidal pseudovariety V.

Language: English

Type (Professor's evaluation): Scientific