Abstract: It is proved that every nonzero ideal in a finite-dimensional semi-simple algebra over a field is generated by an unique central idempotent. Applying this result it is proved that for arbitrary finite group G and arbitrary field Fwhich characteristic does not divide |G|, the only ideal in the group algebra F[G] that is both self-orthogonal and reversible is the zero ideal.

Key words: semi-simple algebra, group algebra, self-orthogonal ideal, reversible ideal

摘要： 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。运用这一结果证明了对于任一有限群G 和特征不能整除|G|的域F，群代数F［G］里既自正交又可逆的理想只有零理想。

关键词: 半单代数, 群代数, 自正交理想, 可逆理想