Some Studies On Griss Algebras

This paper is consisted of four chapters. Chapter I is devoted to introduce some basic theory of BCK-algebra and Griss algebra. In chapter II, the notion of strong Griss algebra is put forward. The quotient algebra of Griss algebra is obtained by constructing a congruence which is induced by an ideal of Griss algebra. In chapter III , first, the regular part of Griss algebra is studied and has been proved be a subalgebra. Second, the definition of generated ideal is introduced . And we get it's represention. In the last chapter, several methods of extension of Griss algebra are given. Some theorems are prepared for classifying the Griss algebras of order n,n ≤ 5. Finally, we surprise to find that the Griss algebras of order n, n ≤ 5 are all strong. Thus we may reasonably believe that strong Griss algebras occupy a large part of Griss algebras.