Weakly abundant semigroups within certain subsemigroups of the semigroup of full contraction mappings of a finite chain
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-preser...
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World Scientific Publishing
2025-01-01
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| Series: | Mathematics Open |
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| Online Access: | https://www.worldscientific.com/doi/10.1142/S2811007225500087 |
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| author | M. M. Zubairu A. Umar A. Jibrin |
| author_facet | M. M. Zubairu A. Umar A. Jibrin |
| author_sort | M. M. Zubairu |
| collection | DOAJ |
| description | 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]. |
| format | Article |
| id | doaj-art-452871d7f0ed4a14a2fc19c56cb00cbc |
| institution | DOAJ |
| issn | 2811-0072 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | World Scientific Publishing |
| record_format | Article |
| series | Mathematics Open |
| spelling | doaj-art-452871d7f0ed4a14a2fc19c56cb00cbc2025-08-20T02:40:32ZengWorld Scientific PublishingMathematics Open2811-00722025-01-010410.1142/S2811007225500087Weakly abundant semigroups within certain subsemigroups of the semigroup of full contraction mappings of a finite chainM. M. Zubairu0A. Umar1A. Jibrin2Department of Mathematics, Bayero University Kano, P.O. Box 3011, Kano, NigeraDepartment of Mathematical Sciences, Khalifa University, P.O. Box 127788, Sas al Nakhl, Abu Dhabi, UAEDepartment of Mathematics, Bayero University Kano, P.O. Box 3011, Kano, NigeraLet [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].https://www.worldscientific.com/doi/10.1142/S2811007225500087Full contraction maps on chainweakly abundant semigroupcontractive refinementcontractive convex refinement |
| spellingShingle | M. M. Zubairu A. Umar A. Jibrin Weakly abundant semigroups within certain subsemigroups of the semigroup of full contraction mappings of a finite chain Mathematics Open Full contraction maps on chain weakly abundant semigroup contractive refinement contractive convex refinement |
| title | Weakly abundant semigroups within certain subsemigroups of the semigroup of full contraction mappings of a finite chain |
| title_full | Weakly abundant semigroups within certain subsemigroups of the semigroup of full contraction mappings of a finite chain |
| title_fullStr | Weakly abundant semigroups within certain subsemigroups of the semigroup of full contraction mappings of a finite chain |
| title_full_unstemmed | Weakly abundant semigroups within certain subsemigroups of the semigroup of full contraction mappings of a finite chain |
| title_short | Weakly abundant semigroups within certain subsemigroups of the semigroup of full contraction mappings of a finite chain |
| title_sort | weakly abundant semigroups within certain subsemigroups of the semigroup of full contraction mappings of a finite chain |
| topic | Full contraction maps on chain weakly abundant semigroup contractive refinement contractive convex refinement |
| url | https://www.worldscientific.com/doi/10.1142/S2811007225500087 |
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