It is proved that every nonzero ideal in a finite - dimensional semi - simple algebra over a field is generated by an unique central idempotent 证明了域上有限维半单代数的每一个非零理想由唯一的中心幂等元生成。
The basic properties of matrix subalgebra were investiaged , the matrix subalgebra was generated by a single matrix , all maximal ideals were classified , the necessary and sufficient conditions for the subalgebra to be semisimple algebra were given 摘要研究了由一个矩阵生成的拒阵子代数的基本性质,给出了其极大理想的完全分类及这类子代数是半单代数的充要条件。