INVERTIBLE ELEMENTS IN BCK-ALGEBRAS

Abstract

In this article, we introduce the notion of cyclic BCK-algebra and study some of its main properties.  In addition, we obtain a structure theorem for bounded commutative of finite order and use it to prove a Lagrange-like theorem for the above class of algebras. Finally, we use the notion of invertible elements to obtain a new characterization of implicative BCK-algebras and study the intersection of all maximal ideals of bounded BCK-algebras.