New generalizations of BCI, BCK and Hilbert algebras

We introduce more generalizations of BCI, BCK and of Hilbert algebras, with proper examples, and show the hierarchies existing between all these algebras, old and new ones. Namely, we found thirty one new generalizations of BCI and BCK algebras and twenty generalizations of Hilbert algebras.Comment: Open problems 11.3 (1), (2), (3) were solved. New (20'), (21''), Theorems 2.4,2.6, Cor. 2.5, 5.5 adde

Relatively compatible operations in BCK-algebras and some related algebras

Let A be a BCK-algebra and f : Ak → A a function. The main goal of this paper is to give a necessary and sufficient condition for ƒ to be compatible with respect to every relative congruence of A. We extend this result in some related algebras, as for example in pocrims.Facultad de Ciencias Exacta