Missouri Journal of Mathematical Sciences

Cubic Implicative Ideals of $BCK$-algebras

Tapan Senapati and K. P. Shum

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Abstract

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.

Article information

Source
Missouri J. Math. Sci., Volume 29, Issue 2 (2017), 125-138.

Dates
First available in Project Euclid: 15 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.mjms/1513306826

Digital Object Identifier
doi:10.35834/mjms/1513306826

Mathematical Reviews number (MathSciNet)
MR3737292

Zentralblatt MATH identifier
06905060

Subjects
Primary: 06F35: BCK-algebras, BCI-algebras [See also 03G25]
Secondary: 03G25: Other algebras related to logic [See also 03F45, 06D20, 06E25, 06F35] 94D05: Fuzzy sets and logic (in connection with questions of Section 94) [See also 03B52, 03E72, 28E10]

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

Citation

Senapati, Tapan; Shum, K. P. Cubic Implicative Ideals of $BCK$-algebras. Missouri J. Math. Sci. 29 (2017), no. 2, 125--138. doi:10.35834/mjms/1513306826. https://projecteuclid.org/euclid.mjms/1513306826


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