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May 2018 Cubic Commutative Ideals of $BCK$-algebras
Tapan Senapati, K. P. Shum
Missouri J. Math. Sci. 30(1): 5-19 (May 2018). DOI: 10.35834/mjms/1534384948

Abstract

In this paper, we apply the concept of cubic set to commutative ideals of $BCK$-algebras, and then characterize their basic properties. We discuss relations among cubic commutative ideals, cubic subalgebras, and cubic ideals of $BCK$-algebras. We provide a condition for a cubic ideal to be a cubic commutative ideal. We define inverse images of cubic commutative ideals and establish how the inverse images of a cubic commutative ideal becomes a cubic commutative ideal. We introduce products of cubic $BCK$-algebras. Finally, we discuss the relationships between (cubic) commutative ideals, implicative ideals, and positive implicative ideals in $BCK/BCI$-algebras.

Citation

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Tapan Senapati. K. P. Shum. "Cubic Commutative Ideals of $BCK$-algebras." Missouri J. Math. Sci. 30 (1) 5 - 19, May 2018. https://doi.org/10.35834/mjms/1534384948

Information

Published: May 2018
First available in Project Euclid: 16 August 2018

zbMATH: 1392.06016
MathSciNet: MR3844386
Digital Object Identifier: 10.35834/mjms/1534384948

Subjects:
Primary: 06F35
Secondary: 03G25, 94D05

Rights: Copyright © 2018 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.30 • No. 1 • May 2018
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