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

Authors : Dawood KHAN, Abdul REHMAN

Pages : 1-10

Doi:10.53570/jnt.798677

View : 17 | Download : 9

Publication Date : 2021-06-30

Article Type : Research Paper

Abstract :In the present manuscript, we introduce the concept of a discrete dynamical system insert ignore into journalissuearticles values(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