有限维交换结合代数的 σ-半单结构

σ-SEMISIMPLE STRUCTURE OF FINITE DIMENSION COMMUTATIVE ASSOCIATIVE ALGEBRAS

通过引入有限维交换结合代数的σ＿自同态映射，研究了σ＿半单代数和σ＿幂零代数的结构。利用σ＿幂零元、σ＿幂等元、σ＿理想和σ＿子代数的直积，我们证明了有限维交换结合σ＿半单代数的结构定理的存在性与唯一性。

This paper introduces the σ_automorphism for finite dimensional commutative associative algebras and studies the structure of σ_semisimple algebras and σ_nilpotent algebras.In addition,by using the σ_nilpotent element,σ_idempotent element,σ_ideal and the direct sum of σ_subalgebra,the existence and uniqueness of the theorem for the structure of finite dimensional commutative associative σ_semisimple algebras is proved.