Open Access
November 2017 Cubic Implicative Ideals of $BCK$-algebras
Tapan Senapati, K. P. Shum
Missouri J. Math. Sci. 29(2): 125-138 (November 2017). DOI: 10.35834/mjms/1513306826


In this paper, we apply the concept of cubic sets to implicative ideals of $BCK$-algebras, and then characterize their basic properties. We discuss relations among cubic implicative ideals, cubic subalgebras and cubic ideals of $BCK$-algebras. We provide a condition for a cubic ideal to be a cubic implicative ideal. We define inverse images of cubic implicative ideals and establish how the inverse images of a cubic implicative ideal become a cubic implicative ideal. Finally we introduce products of cubic $BCK$-algebras.


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Tapan Senapati. K. P. Shum. "Cubic Implicative Ideals of $BCK$-algebras." Missouri J. Math. Sci. 29 (2) 125 - 138, November 2017.


Published: November 2017
First available in Project Euclid: 15 December 2017

zbMATH: 06905060
MathSciNet: MR3737292
Digital Object Identifier: 10.35834/mjms/1513306826

Primary: 06F35
Secondary: 03G25 , 94D05

Keywords: $BCK$-algebra , cubic ideal , cubic implicative ideal , cubic set , cubic subalgebra

Rights: Copyright © 2017 Central Missouri State University, Department of Mathematics and Computer Science

Vol.29 • No. 2 • November 2017
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