U – Algebras: A Study and Applications

Abstract

The notion of BCK (Brain Computer Kolmogorov) algebras was originated by K. Is´eki and S. Tanaka [2 and 3], from two different ways: (1) set theory, and (2) classical and non-classical propositional calculi. The BCK-operation * is an analogue of the set theoretical difference. Now a days BCK-algebras have been studied by many authors and they have been applied to many branches of mathematics, such as group theory, functional analysis, probability theory, topology, fuzzy set theory, and so on. Many researchers have developed several results using BCK/BCI/BCH algebras.

In this paper we introduce the concept of U – algebra and study its properties with examples. Main results of the paper is “The class of all positive BCH – algebras on a finite set E is an U – algebra under a suitable binary operation”.