代数闭域上三维交换代数的分类  

The Classification of 3-Dimensionally Commutative Algebras on Algebraically Closed Field

作　　者：程智[1] 孙翠芳[1] 

机构地区：[1]安徽师范大学数学计算机科学学院,安徽芜湖241000

出　　处：《安徽师范大学学报（自然科学版）》2008年第3期205-207,共3页Journal of Anhui Normal University(Natural Science)

基　　金：安徽师范大学青年基金(2005xqn04;2007xqn52)

摘　　要：研究了代数闭域上三维交换代数的分类.在已有二维代数分类的基础上,获得了代数闭域K上基为{e,a,b}的三维交换代数A的分类:对于b=a2的情况,有三种类型:对于b≠a2的情况,有九种类型.In this paper, we discuss the classification of 3-dimensionally commutative algebras on algebraically closed field. By using the results of the classification of 2-dimensional algebras, we prove that, for the commutative algebra with bases ｜ e, a, b ｜ on algebraically closed field, there are three kinds of algebras for the case of b = a^2 and nine kinds of algebras for the case of b ≠ a^2 .

关 键 词：代数闭域 三维代数 分类 

分 类 号：O152.6[理学—数学]