Relatively free *-bands

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

Authors

Petrich, M (Author) Other; Pedro V. Silva (Author) FCUP

Journal

Title: Beitrage zur Algebra und Geometrie

Vol. 41 No. 2

Pages: 569-588

ISSN: 0138-4821

Publisher: Springer Nature

Indexing

Scopus - 3 Citations

Other information

Authenticus ID: P-009-KDZ

Abstract (EN): A *-band is an algebra consisting of a band (idempotent semigroup) on which an involution * is defined satisfying an extra condition; in summary (xy)* = y*x*, x** = x, x = xx*x, (xy)z = x(yz), x2 = x. The lattice of all *-band varieties was determined by Adair who also provided a basis for the identities of each variety. Another system of bases was devised by Petrich. Defining certain operators on the free involutorial semigroup F on a nonempty set X, we construct a system of fully invariant congruences on F which is in bijection with the set of all proper *-band varieties, with the exception of normal *-band varieties which require a different treatment. The proof of this result is based on those evoked above and is broken into a long sequence of lemmas. © 2000 Heldermann Verlag.

Language: English

Type (Professor's evaluation): Scientific