关键词: 半单代数, 群代数, 自正交理想, 可逆理想

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