Work

Weakly abundant semigroups within certain subsemigroups of the semigroup of full contraction mappings of a finite chain

Year: 2025

Type: article

Abstract: Let [Formula: see text] be a finite n-chain [Formula: see text], and let [Formula: see text] be the monoid of full contraction mappings on [Formula: see text]. Denote by [Formula: see text] and [Formula: see text] to be the monoid of order-decreasing full contractions, the monoid of all order-preserving full contractions, the monoid of all order-preserving or order-reversing full contractions, and the monoid of all order-decreasing and order-preserving full contraction mappings on [Formula: see text], respectively. In this paper, we characterize the generalized starred Green’s relations [Formula: see text] and [Formula: see text] on every monoid [Formula: see text], and show that for any monoid [Formula: see text], S is both weakly abundant and weakly [Formula: see text]-unipotent, while for any monoid [Formula: see text], it is neither. This further demonstrates that the decreasing property affects the weakly abundance property on any [Formula: see text].

Source: Mathematics Open

DOI: 10.1142/s2811007225500087

Authors: M. M. Zubairu, A. Umar, A. Jibrin

Institutions: Bayero University Kano, Khalifa University of Science and Technology

Language: English

Topic: semigroups and automata theory

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4411285081

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Cites: 17

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Related to: 10