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.
"Cubic Implicative Ideals of $BCK$-algebras." Missouri J. Math. Sci. 29 (2) 125 - 138, November 2017. https://doi.org/10.35834/mjms/1513306826