BCI-implicative ideals of BCI-algebras

This paper introduces the notion of BCI-implicative ideals and characterizes BCI-implicative ideals and closed BCI-implicative ideals. Using these characterizations, the connections between BCI-implicative ideals and other ideals in BCI/BCK-algebras are investigated. Additionally, the extension property of BCI-implicative ideals is established. Finally, the implicative BCI-algebras are completely described using BCI-implicative ideals. The above work generalizes the corresponding results in BCK-algebras.