A New View of Homomorphic Properties of BCK-Algebra in Terms of Some Notions of Discrete Dynamical System

Year 2021, Issue: 35, 1 - 10, 30.06.2021

Dawood Khan Abdul Rehman

https://doi.org/10.53570/jnt.798677

Abstract

In the present manuscript, we introduce the concept of a discrete dynamical system (Ⱬ,Ψ) in BCK-algebra where Ⱬ is a BCK-algebra and Ψ is a homomorphism from Ⱬ to Ⱬ and establish some of their related properties. We prove that the set of all fixed points and the set of all periodic points in BCK-algebra Ⱬ are the BCK-subalgebras. We show that when a subset of BCK-algebra Ⱬ is invariant concerning Ψ. We prove that the set of all fixed points and the set of all periodic points in commutative BCK-algebra Ⱬ with relative cancellation property are the ideals of Ⱬ. We also prove that the set of all fixed points in Ⱬ is an S-invariant subset of a BCK-algebra Ⱬ.

Keywords

BCK-Algebra, S-invariant or (Strongly invariant) set., discrete dynamical system, periodic points, fixed points, invariant set, strongly invariant

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