BCK-代数的添零扩张

Extension of a BCK-algebra by Adding a New Zero Element

针对扩张的一种方式———添零扩张进行研究 ,讨论了添零扩张后的BCK -代数与原BCK -代数在关联性、正关联性、有条件 (S)等性质上的联系 ,并用定理的形式给出了一些重要结论。利用这些结论 ,能很方便地从低阶BCK -代数的已知性质来推断高阶BCK

The extension of a BCK-algebra is an important aspect of the study of the BCK-algebra. In this paper, the extension of a BCK-algebra by adding a new zero element is discussed in a comprehensive way. Some results about the relations among the characters of implicative, positive implicative, commutative etc. in the original BCK-algebra and those in the extension are explicitly presented. Making use of these results, we can conveniently obtain the characters of a BCK-algebra of a higher order from the known characters of a BCK-algebra of a lower order.