关于BCI-代数的商代数的几点注记

NOTES ON THE QUOTIENT ALGEBRAS OF BCI—ALGEBRAS

设 X 为一个 BCI-代数,N,H 为 X 的理想,A 为 X 的子代数,X/N 为通常意义下的商代数,C_0为 X/N 的常元,C_0(?)H(?)N(?)A.今A/N={C_x∈X/N|x∈A}本文主要证明了以下几个结果:i)X/N=X/H;ii)A/N(?)A/N;iii)当 A 还是 X 的理想时,A/N=A/N.

In this paper we have mainly proved the following: Let X be a BCI-algebra,N and H ideals of X,A a sub-algebra of X, X/N the quotient algebra as usual,C_0 the constant ele ment of X/N,C_0■H■N■A,and(A/N)={C_x∈X/N|x∈A},then we have i)X/N=X/H; ii)(A/N)■A/N iii)Moreover,if A is a ideal of X,then (A/N)=A/N.