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

Dawood Khan; Abdul Rehman

doi:10.53570/jnt.798677

EN

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

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

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Dawood Khan ^*
0000-0002-6850-6783
Pakistan

Abdul Rehman This is me
0000-0003-2569-8540
Pakistan

Publication Date

June 30, 2021

Submission Date

September 22, 2020

Acceptance Date

May 21, 2021

Published in Issue

Year 2021 Number: 35

DOI

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

IZ

https://izlik.org/JA87YA36KU

APA

Khan, D., & Rehman, A. (2021). A New View of Homomorphic Properties of BCK-Algebra in Terms of Some Notions of Discrete Dynamical System. Journal of New Theory, 35, 1-10. https://doi.org/10.53570/jnt.798677

AMA

1.Khan D, Rehman A. A New View of Homomorphic Properties of BCK-Algebra in Terms of Some Notions of Discrete Dynamical System. JNT. 2021;(35):1-10. doi:10.53570/jnt.798677

Chicago

Khan, Dawood, and Abdul Rehman. 2021. “A New View of Homomorphic Properties of BCK-Algebra in Terms of Some Notions of Discrete Dynamical System”. Journal of New Theory, nos. 35: 1-10. https://doi.org/10.53570/jnt.798677.

EndNote

Khan D, Rehman A (June 1, 2021) A New View of Homomorphic Properties of BCK-Algebra in Terms of Some Notions of Discrete Dynamical System. Journal of New Theory 35 1–10.

IEEE

[1]D. Khan and A. Rehman, “A New View of Homomorphic Properties of BCK-Algebra in Terms of Some Notions of Discrete Dynamical System”, JNT, no. 35, pp. 1–10, June 2021, doi: 10.53570/jnt.798677.

ISNAD

Khan, Dawood - Rehman, Abdul. “A New View of Homomorphic Properties of BCK-Algebra in Terms of Some Notions of Discrete Dynamical System”. Journal of New Theory. 35 (June 1, 2021): 1-10. https://doi.org/10.53570/jnt.798677.

JAMA

1.Khan D, Rehman A. A New View of Homomorphic Properties of BCK-Algebra in Terms of Some Notions of Discrete Dynamical System. JNT. 2021;:1–10.

MLA

Khan, Dawood, and Abdul Rehman. “A New View of Homomorphic Properties of BCK-Algebra in Terms of Some Notions of Discrete Dynamical System”. Journal of New Theory, no. 35, June 2021, pp. 1-10, doi:10.53570/jnt.798677.

Vancouver

1.Dawood Khan, Abdul Rehman. A New View of Homomorphic Properties of BCK-Algebra in Terms of Some Notions of Discrete Dynamical System. JNT. 2021 Jun. 1;(35):1-10. doi:10.53570/jnt.798677