Regular semigroups weakly generated by set

• Type: Article in International Scientific Journal
• Date: 2024

Authors

Luís Oliveira (Author) FCUP

Journal

Title: Semigroup Forum

ISSN: 0037-1912

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 0 Citations

Scopus - 0 Citations

Other information

Authenticus ID: P-017-55Y

DOI: 10.1007/s00233-024-10475-1

Abstract (EN): We prove the existence and uniqueness (up to isomorphism) of a regular semigroup F(X)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\,\textrm{F}\,}}(X)$$\end{document} weakly generated by a set X of elements such that all other regular semigroups weakly generated by X are homomorphic images of F(X)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\,\textrm{F}\,}}(X)$$\end{document}. The semigroup F(X)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\,\textrm{F}\,}}(X)$$\end{document} is introduced by a presentation and the word problem for that presentation is solved. The structure of the semigroup F(X)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\,\textrm{F}\,}}(X)$$\end{document} is also studied.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 30