诣零BCI代数的构造(英文)

Structure of the Nil BCI Algebras

证明了一个分支Ａ（ｅ）一旦有一个元素属于Ｎｋ（Ｘ）＝∪ｅ∈ＥｋＡ（ｅ）或Ｎ（Ｘ）＝∪ｅ∈ＥｆＡ（ｅ），那么这个分支Ａ（ｅ）以及它的相伴分支Ａ（０＊ｅ）都将整个地被包含于Ｎｋ（Ｘ）或Ｎ（Ｘ）。

Let X be a BCI algebra, B and E be its BCK part and p semisimple part respectively. In this note, we investigated the structure of N k(X) and N(X) , from the angle of branches, proved that once there is an element of a branch A(e) which belongs to N k(X) , then this branch A(e) and its conjugate branch A(0*e) will be contained wholly by N k(X) . Therefore, the structure of N k(X) and N(X) are determined completely by N k(E) = E k and N(E) = E f . It is ture that N k(X)=∪e∈E k A(e) , N(X)=∪e∈E fA(e) .