Application of Lattice Theory on Order-Preserving Full Transformation Semigroup Via Fixed Points
| dc.contributor.author | Ibrahim, G. R.1, Bakare, G. N.2, Akinwunmi. S. A.3and Aliu, O. T. | |
| dc.date.accessioned | 2025-01-29T04:52:06Z | |
| dc.date.available | 2025-01-29T04:52:06Z | |
| dc.date.issued | 2023 | |
| dc.description.abstract | Let 𝑋𝑛be a finite set, 𝑇𝑛be full transformation semigroup and 𝑂𝑇𝑛be subsemigroup of all order-preserving full transformation semigroup. Let transformation𝛼∈𝑂𝑇𝑛∶(∀𝑥,𝑦∈Dom𝛼),if𝑥≤𝑦then𝛼(𝑥)≤𝛼(𝑦), then 𝛼is called order-preserving transformation. This paper focuses on the notion of fixed points which are elements that remain unchanged under this transformation. That is, 𝛼(𝑥)=𝑥where 𝛼is a transformation on 𝑂𝑇𝑛, 𝑥is the point in the 𝐷𝑜𝑚(𝛼)and 𝛼(𝑥)is the image of x,∀x∈αThe existence of fixed points was explored and emphasizing their role in establishing a lattice structure. The lattice of fixed points exhibits two essential operations: meet and join. These operations enable us to compute the greatest and least elements of fixed points. Beyond pure mathematics, the study of fixed points and their lattice structure has applications in dynamical systems, economics, computer science, and several other domains, making it both a theoretical and practical subject. | |
| dc.identifier.issn | 2408 –4840 | |
| dc.identifier.uri | https://kwasuspace.kwasu.edu.ng/handle/123456789/3701 | |
| dc.language.iso | en | |
| dc.publisher | Faculty of Physical Sciences, University of Ilorin | |
| dc.relation.ispartofseries | 10 | |
| dc.title | Application of Lattice Theory on Order-Preserving Full Transformation Semigroup Via Fixed Points | |
| dc.type | Article |
Files
Original bundle
1 - 1 of 1
Loading...
- Name:
- View of Application of Lattice Theory on Order-Preserving Full Transformation Semigroup Via Fixed Points.htm
- Size:
- 4.78 KB
- Format:
- Hypertext Markup Language
- Description:
License bundle
1 - 1 of 1
Loading...
- Name:
- license.txt
- Size:
- 1.71 KB
- Format:
- Item-specific license agreed to upon submission
- Description: