【摘要】 本文将讨论半单优BCI-代数的性质。我们得到了如下主要的结果: (1) 一个非零优BCI-代数X是半单的充要条件是X为单理想的次直积。 (2) 设X是一个非零半单优BCI-代数,则如下命题是等价的: ⅰ,X可写成有限个单理想的次直积。ⅱ,X是Noether的。ⅲ,X是Artin的。更多还原

【Abstract】 In this paper we consider the properties of semi-simple well BCI-algebras. We obtain the following interesting results:1) Let X≠0 be a well BCI-algebra. Then X is a semi-simple if and only if X can be written as a quasi-direct product of simple ideals of X.2) Let X≠0 be a semi-simple well BCI-algebra. Then the following statements are eguivalent:(ⅰ) X can be written as a quasi-direct product of a finite number of simple ideals of X.(ⅱ) X is Noetherian.(ⅲ) X is Artinian.更多还原