In this paper we introduce the notion of n-fold BCI-positive implicative ideals in
BCI-algebras and study some properties. We also establish the extension properties
of n-fold BCI-positive implicative ideals. We use the notion of n-fold BCI-positive
implicative ideals to completely describe n-fold BCI-algebras. This work generalizes
the corresponding results in BCK/BCI-algebras.