On *-bands and their varieties

• Type: Article in International Scientific Journal
• Date: 2003

Authors

Mario Petrich (Author) Other; Pedro V. Silva (Author) FCUP

Journal

Title: Rocky Mountain Journal of Mathematics

Vol. 33 No. 1

Pages: 217-252

ISSN: 0035-7596

Publisher: Rocky Mountain Mathematics Consortium

Indexing

ISI Web of Knowledge - 1 Citation

ISI Web of Science

Scopus - 1 Citation

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-000-HPF

DOI: 10.1216/rmjm/1181069994

Abstract (EN): A *-band is a semigroup with a unary operation * obeying the axioms (xy)* = y*x*, x** = x, x = xx*x, x(2) = x. On a free involutorial semigroup F on a nonempty set X, we define a family of operators delta(tn) and prove that each of them is a *-homomorphism of F onto its image with a suitable multiplication and the *-operation of F. We then investigate the interplay of this operator with several others occurring in the literature as well as the relationship of the equivalence relations they induce on F or on X+. In particular, we obtain the structural description of all relatively free *-bands. We conclude with a brief consideration of the problem of converting *-identities to equivalent star-free identities.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 36