ON DERIVATIONS OF BE-ALGEBRAS

In this paper, we introduce the notion of derivationin a BE-algebra, and consider the properties of derivations. Also,we characterize the xed set Fix d (X) and Kerd by derivations.Moreover, we prove that if d is a derivation of BE-algebra, every lter F is a d-invariant. 1. IntroductionY. Imai and K. Is eki introduced two classes of abstract algebras:BCK-algebras and BCI-algebras([3, 4]). It is known that the class ofBCK-algebras is a proper subclass of the class of BCI-algebras. In [1,2], Q. P. Hu and X. Li introduced a wide class of abstracts: BCH-algebras. They have shown that the class of BCI-algebras is a propersubclass of the class of BCH-algebras. In [5], H. S. Kim and Y. H. Kimintroduced the notion of a BE-algebra as a dualization of a generation ofa BCK-algebras. In this paper, we introduced the notion of derivationin a BE- algebra, and considered the properties of derivations. Also, wecharacterized the xed set Fix d (X) and Kerd by derivations. Moreover,we prove that if d is a derivation of BE-algebra, every lter F is a d-invariant.2. PreliminariesIn what follows, let X denote an BE-algebra unless otherwise speci- ed.