摘要
本文的主要结论是:1.设X是一个BCK-代数。下列断言是等价的:a.X是反单的;b.X的任一同态象都是幂零心BCK-代数的亚直和;c.X中不存在素理想P使X/P有极小理想;d.X的任一理想的同态象都不是单BCK-代数。2.设X是一个BCK-代数。X是反单的当且仅当Vx∈X,y∈(x)~2,(x)=(x*y)。
In this paper,the main results as fellows:1.Let X is a BCK-algebra.Thefollowing conditions are equivalent:1)X is antisimple;2)Every homomorphicimage of X is a subdirect sum of nilpotent heart BCK-algebras;3)X does netcontain a prime ideal P such that X/P has a minimal ideal;4)No ideal of Xcan be homomorphically mapped onto a simple BCK-algebra.2.Let X is a BCK-algebra,then X is antisimple if and only if ∨x∈X,y∈(x)~2,(x)=(x*y).
出处
《晓庄学院自然科学学报》
CAS
1991年第2期102-104,132,共4页
Journal of Natural Science of Hunan Normal University
关键词
BCK-代数
理想
根基
亚直和
同态
algebra
ideal(mathematics)
radical
subdirect products
homomorphism/BCK-algebra
