Regular semigroups weakly generated by idempotents

• Type: Article in International Scientific Journal
• Date: 2023

Authors

Luís Oliveira (Author) FCUP

Journal

Title: International Journal of Algebra and Computation

Vol. 33

Pages: 851-891

ISSN: 0218-1967

Publisher: World Scientific

Indexing

ISI Web of Knowledge - 1 Citation

Scopus - 1 Citation

Other information

Authenticus ID: P-00Y-PDF

DOI: 10.1142/s0218196723500388

Abstract (EN): A regular semigroup is weakly generated by a set X if it has no proper regular subsemigroup containing X. In this paper, we study the regular semigroups weakly generated by idempotents. We show there exists a regular semigroup FI(X) weakly generated by |X| idempotents such that all other regular semigroups weakly generated by |X| idempotents are homomorphic images of FI(X). The semigroup FI(X) is defined by a presentation ? GX,?(e) ? ?(s)? and its structure is studied. Although each of the sets GX, ?(e), and ?(s) is infinite for |X|=2, we show that the word problem is decidable as each congruence class has a canonical form. If FIn denotes FI(X) for |X| = n, we prove also that FI2 contains copies of all FIn as subsemigroups. As a consequence, we conclude that (i) all regular semigroups weakly generated by a finite set of idempotents, which include all finitely idempotent generated regular semigroups, strongly divide FI2; and (ii) all finite semigroups divide FI2.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 41