Abstract. In this note, we show that every linear BCI -algebra( X ; ⁄;e ), e 2 X , has of the form x ⁄ y = x i y + e where x;y 2 X ,where X is a fleld with jX j ‚ 3. 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 classof BCK -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 abstract algebras: BCH -algebras. They have shown that the class of BCI -algebras is aproper subclass of the class of BCH -algebras. J. Neggers and H. S.Kim introduced the notion of B -algebras ([8, 9]), i.e., (I) x ⁄ x = e ;(II) x ⁄ e = x ; (III) ( x ⁄ y ) ⁄ z = x ⁄ ( z ⁄ ( e ⁄ y )), for any x;y;z 2 X .C. B. Kim and H. S. Kim ([5]) introduced the notion of a BG -algebraswhich is a generalization of B-algebras, and constructed a BG -algebrafrom a non-empty set, which is non-group-derived. A. Walendziak ([12])introduced a new notion, called an BF -algebra, i.e., (I); (II) and (IV)