Relatively free bands

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

Authors

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

Journal

Title: Communications in Algebra

Vol. 28 No. 5

Pages: 2615-2631

ISSN: 0092-7872

Publisher: Taylor & Francis

Indexing

ISI Web of Knowledge - 5 Citations

ISI Web of Science

Scopus - 4 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-001-19Z

DOI: 10.1080/00927870008826982

Abstract (EN): The operators h(n) and i(n) and their duals <(h(n))over bar> and <(i(n))over bar> defined on the free semigroup X+ for a nonempty set X by Gerhard and Petrich are proved here to be homomorphisms of X+ onto certain subsets of X+ with a suitable multiplication. From the work of the authors mentioned, these operators induce fully invariant congruences on X+ corresponding to join irreducible varieties of bands if X is countably infinite. New operators on X+ are defined by means of these operators which give homomorphisms in an analogous way and induce fully invariant congruences on X+ corresponding to all varieties of bands except. For the variety of all bands, and some varieties of normal bands. The Former of these was investigated by the mentioned authors and the latter must be treated differently. By means of the above operators we are able to characterize all cases of relatively free bands.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 17