关于正关联BCK代数的一种扩张

The Condition (S)Extension of Positive Implicative BCK-Algebras

英文关键词:positive implicative BCK-algebra  implicative BCK- algebra  BCK-algebrawith the condition （S）  BCI-endomorphism  semigroup.

中文摘要:

      在本文中，证明了每一个正关联ＢＣＫ－代数Ｘ均可嵌入于具有条件（Ｓ）的正关联ＢＣＫ－代数Ｘ^*，且Ｘ是Ｘ^*的一个子代数．特别地，当Ｘ是关联时，那么Ｘ^*也是关联的

英文摘要:

      In this note, we prove that every positive implicative BCK-algebra X canbe imbedded in a positive implicative BCK-algebra X with the condition (S), and X isa subalgebra of X^*. In particular, whenever X is implicative, so is X^*.