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An Observation on the Natural Partial Order of Transformation Semigroups Restricted by an Equivalence Relation |
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| รหัสดีโอไอ | |
| Creator | Piyaporn Tantong |
| Title | An Observation on the Natural Partial Order of Transformation Semigroups Restricted by an Equivalence Relation |
| Contributor | Nares Sawatraksa |
| Publisher | Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi |
| Publication Year | 2565 |
| Journal Title | Progress in Applied Science and Technology |
| Journal Vol. | 12 |
| Journal No. | 1 |
| Page no. | 17-22 |
| Keyword | Natural partial order, Maximal element, Minimal element, Covering element |
| URL Website | https://ph02.tci-thaijo.org/index.php/past/index |
| Website title | Progress in Applied Science and Technology |
| ISSN | 2730-3020 |
| Abstract | Let T(X) be the full transformation semigroup of a set X. We consider the subsemigroup of T(X) defined by E(X,σ)={α∈T(X):∀x,y∈X,(x,y)∈σ implies xα=yα} for an arbitrary equivalence relation σ on X. The natural partial order on the largest regular subsemigroup of E(X,σ) is discussed in this paper, and we characterize when two regular elements of E(X,σ) are related under this order. Also, their maximal, minimal and covering elements are described. |
