有限BCK-代数子代数个数估计定理

设X是一个n阶BCK-代数,我们用N(i)来表示X中i阶子代数的个数,其中1≤i≤n.本文的目的是证明有限BCK-代数子代数个数估计定理. 定理 设X是n(≥1)阶BCK-代数,则,i=1,2,…,n. 关于BCK-代数的定义和基本性质可参阅文献1]和2].为了引用的方便,我们列出一个BCK-代数必须满足的五条公理:

A Theorem on the Estimation of the Number of Subalgebras in a Finite BCK-Algebra

Let X be a BCK-algebra of order n. We denote the number of subal-gebras of order i in X by N(i). In this paper we prove the following theorem which estimates the number of subalgebras in a finite BCK-algebra. Theorem. Let X be a BCK-algebra of order n. Then we have