Missouri Journal of Mathematical Sciences
- Missouri J. Math. Sci.
- Volume 29, Issue 2 (2017), 125-138.
Cubic Implicative Ideals of $BCK$-algebras
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.
Missouri J. Math. Sci., Volume 29, Issue 2 (2017), 125-138.
First available in Project Euclid: 15 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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