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Ganyushkin, Olexandr; Mazorchuk, Volodymyr

doi:10.1007/978-1-84800-281-4_9

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Introduction/ Background1

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2021

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“…Various special sub-semigroups of partial transformation semigroups have been studied by many researcher(s) like [2], [3] and [4] but few have work on contraction mapping being a new class of transformation semigroup. The relationship between fix of and idempotency was study by [4] for ∈ and the equivalence relation {( , ) ∈ 2 ∶ = } is denoted by ( ).…”

Section: Introduction/ Backgroundmentioning

confidence: 99%

Nildempotency Structure of Partial One-One Contraction 𝐶𝐼𝑛 Transformation Semigroups

Akinwunmi¹,

Mogbonju²,

Adeniji³

et al. 2021

IJRSI

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The principal objects of interest in the current research are the finite sets and the contraction finite transformation semigroups and the characterization of nildempotent elements in . Let be a finite set, say = { , , … }, where is a non-negative integer then ∈ for which for all , ∈ , | − | ≤ | − | is a contraction mapping for all , ∈ , provided that any element in ( ) is not assumed to be mapped to empty as a contraction. We show that ∈ is nildempotent if there exist some minimal (nildempotent degree) , ∈ such that = ∅ ⟹ = where = then = = = ∅ implies ⊆ | ( )| where = for each ∈ . Then = − + , , ∈ for 1≥ ≥ .

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Section: Introduction/ Backgroundmentioning

confidence: 99%