Missouri Journal of Mathematical Sciences

Cubic Commutative Ideals of $BCK$-algebras

Tapan Senapati and K. P. Shum

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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.

Article information

Source
Missouri J. Math. Sci., Volume 30, Issue 1 (2018), 5-19.

Dates
First available in Project Euclid: 16 August 2018

Permanent link to this document
https://projecteuclid.org/euclid.mjms/1534384948

Digital Object Identifier
doi:10.35834/mjms/1534384948

Mathematical Reviews number (MathSciNet)
MR3844386

Zentralblatt MATH identifier
1392.06016

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 commutative ideal

Citation

Senapati, Tapan; Shum, K. P. Cubic Commutative Ideals of $BCK$-algebras. Missouri J. Math. Sci. 30 (2018), no. 1, 5--19. doi:10.35834/mjms/1534384948. https://projecteuclid.org/euclid.mjms/1534384948


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