Characterization of quasi idempotent in semigroups of full contraction mappings
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Date
2024-02-01
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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 Dom α = Xn. A transformation β ∈ CTn is said to be full contraction mapping if
∀ x, y ∈ Dom α, |xα − yα| ≤ |x − y| ∀ x, y ∈ Dom α. Let CTn be the semigroup of full contraction transformation and let QCTn 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 CTn and later come up with a strong and useful theorem.
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https://flayoophl.com/journals/index.php/pnspsc