Characterization of quasi idempotent in semigroups of full contraction mappings
Loading...
Date
2024
Journal Title
Journal ISSN
Volume Title
Publisher
Nigerian Society of Physical Sciences
Abstract
Let Tn be the semigroup of full transformation of a finite set and let Xn = {1, 2, · · · , n}. A transformation α : Domα ⊂ Xn →Im(α) ⊂ Xn is said to be full or total transformation if Domα = Xn. A transformation β ∈ CT n is said to be full contraction mapping if ∀ x, y ∈ Domα, |xα − yα| ≤ |x − y| ∀ x, y ∈ Domα. Let CT n be the semigroup of full contraction transformation and let QCT n be its quasi-idempotent of full contraction transformation of Xn. In this paper, we characterized quasi-idempotent elements into matching blocks, non-matching blocks and self matching blocks of CT n and later come up with a strong and useful theorem
Description
Keywords
Citation
Characterization of quasi idempotent in semigroups of full contraction mappings AD Adeshola, SO Akande, R Garba-Ibrahim, J Lawal - Proceedings of the Nigerian Society of Physical …, 2024