P-closure ideals in BCI-algebras

In this paper, for any non-empty subset A of a BCI-algebra X, we introduce the concept of p-closure of A, denoted by $$A^{pc}$$ Apc , and investigate some related properties. Applying this concept, we characterize the minimal elements of BCI-algebras. We also give a characterization of the p-closure of subalgebras of X by some branches of X. We state a necessary and sufficient condition for a BCI-algebra (1) to be p-semisimple; (2) to be a BCK-algebra. Moreover, we show that the p-closure can be used to define a closure operator. We investigate the relationship between $$f(A^{pc})$$ f(Apc) and $$(f(A))^{pc}$$ (f(A))pc for a BCI-homomorphism f. Finally, we prove that $$A^{pc}$$ Apc is the least closed p-ideal containing A for any ideal A of X.