THE CONGRUENCE eta* ON SEMIGROUPS

• Type: Article in International Scientific Journal
• Date: 2016

Authors

Shahzamanian, MH (Author) FCUP

Journal

Title: Quarterly Journal of Mathematics

Vol. 67

Pages: 405-423

ISSN: 0033-5606

Publisher: Oxford University Press

Indexing

ISI Web of Knowledge - 1 Citation

Scopus - 1 Citation

Other information

Authenticus ID: P-00M-5AS

DOI: 10.1093/qmath/haw017

Abstract (EN): In this paper, we define a congruence eta* on semigroups. For the finite semigroups S, eta* is the smallest congruence relation such that S/eta* is a nilpotent semigroup (in the sense of Mal'cev). In order to study the congruence relation eta* on finite semigroups, we define a CS-diagonal finite regular Rees matrix semigroup. We prove that if S is a CS-diagonal finite regular Rees matrix semigroup, then S/eta* is inverse. Also, if S is a completely regular finite semigroup, then S/eta* is a Clifford semigroup. We show that, for every non-null principal factor A/B of S, there is a special principal factor C/D such that every element of A\B is eta*-equivalent with some element of C\D. We call the principal factor C/D the eta*-root of A/B. All eta*-roots are CS-diagonal. If certain elements of S act in the special way on the R-classes of a CS-diagonal principal factor, then it is not an eta*-root. Some of these results are also expressed in terms of pseudovarieties of semigroups.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 19