诣零BCI－代数p－半单部分的特征

Characterizations of p semisimple part in nil BCI algebras

讨论了诣零ＢＣＩ－代数ｐ－半单部分ＳＰ（Ｘ）的元素特征，给出诣零ＢＣＩ－代数中ＳＰ（Ｘ）成为理想的两个充要条件，即在诣零代数Ｘ＝Ｎｋ（Ｘ）中，ＳＰ（Ｘ）成为理想当且仅当以下条件之一成立：（ｉ）ｘ∈Ｘ，ｕ∈ＳＰ（Ｘ），若ｘ＊ｕｋ＝０，则ｘ＝０；（ｉ）ｘ∈Ｐ（Ｘ），ｕ∈ＳＰ（Ｘ），若ｘ＊ｕｋ＝０，则ｘ＝０．

The elements characterizaticns of p semisimple part in nil BCI algebras are discussed, and some conditions for which the p semisimple part SP(X) becomes an ideal are given, for a nil algebra X=N k(X) as follows: SP(X) is an ideal if and only if x*u k =0 implies x =0 for any x∈X and u∈SP(X), if and only if x*u k=0 mplies x =0 for any x∈P(X) and u∈SP(X) .