Regular semigroups weakly generated by one element

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

Authors

Luís Oliveira (Author) FCUP

Journal

Title: Semigroup Forum

Vol. 107

Pages: 525-563

ISSN: 0037-1912

Publisher: Springer Nature

Indexing

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Other information

Authenticus ID: P-00Z-5VW

DOI: 10.1007/s00233-023-10389-4

Abstract (EN): In this paper we study the regular semigroups weakly generated by a single element x, that is, with no proper regular subsemigroup containing x. We show there exists a regular semigroup F-1 weakly generated by x such that all other regular semigroups weakly generated by x are homomorphic images of F-1. We define F-1 using a presentation where both sets of generators and relations are infinite. Nevertheless, the word problem for this presentation is decidable. We describe a canonical form for the congruence classes given by this presentation, and explain how to obtain it. We end the paper studying the structure of F-1. In particular, we show that the 'free regular semigroup FI2 weakly generated by two idempotents' is isomorphic to a regular subsemigroup of F-1 weakly generated by {xx', x' x}.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 39