摘要
本文讨论了ZY3代数的理想,并证明了同构定理8,9和11。定理8。设X是ZY3代数。若A是X的一个理想,则有同态f,使得X(?)X/A。定理9。设X_1与X_2是ZY3代数,且X_2中的基本二元关系“≤”是一个偏序。若X_1(?)X_2,则X_1/Ker f≌X_2。定理11。设X是ZY3代数。若A,K是X的理想,A(?)K,则X/A≌X/K/A/K。
In this paper the concept and ideals of ZY3-algebras were introduced, and the following isomorphism theorems were proved.Theorem 8 Let X be a ZY3-algebra. If A is an ideal of X, then X～X/A.Theorem 9 Suppose that X_1 and X_2 are ZY3-algebras and the relation "≤" in X_2 is a partial order. If X_1(?)X_2, then X_1/Ker f(?)X_2.Theorem 11 Let X be a ZY3-algebra. If A, K are ideals of X, A(?)K, then X/A(?)X/K/A/K.
关键词
代数
同构定理
理想ZY3代数
algebra
isomorphism theorem
homomorphism theorem
homomorphic mapping
ideal
first isomorphism theorem
