Several Classes of BCI-algebras and their Properties

We introduce BCI structures which are extensions of 1-sorted structure and are systems 〈 a carrier, an internal complement 〉, where the carrier is a set and the internal complement is a binary operation on the carrier. Let us note that there exists a BCI structure which is non empty and strict. Let A be a BCI structure and let x, y be elements of A. The functor x \ y yielding an element of A is defined by: (Def. 1) x \ y = (the internal complement of A)(x, y). We introduce BCI structures with 0 which are extensions of BCI structure and zero structure and are systems 〈 a carrier, an internal complement, a zero 〉,