BCI-代数的诣零性

ON NIL PROPERTY OF BCI-ALGEBRAS

本文将证明:BCI-代数X的诣零根N(X)正好是它的所有幂零分支的并集,进而得到:X为诣零代数■X的广义结合部分G(X)为诣零代数;X的每个理想为子代数■的每个理想为子代数。此外,本文还讨论了幂零指数的若干性质。

In this paper, we shall prove that the Nil-radical N(X) in a BCI—algebra X is the union of all nilpotent branches in X; X is a nil algebra iff the its genemlized associative part G (X) is a nil algebra. Moreover, we shall discuss some properties of nilpotent exponents.