Self-orthogonal Ideal in Group Algebras
Author(s): QIU Weisheng
Pages: 294-296
Year: 2001 Issue: 3
Journal: ACTA SCIENTIARUM NATURALIUM UNIVERSITATIS PEKINENSIS
Keyword: 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 F which 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.
Pages: 294-296
Year: 2001 Issue: 3
Journal: ACTA SCIENTIARUM NATURALIUM UNIVERSITATIS PEKINENSIS
Keyword: 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 F which 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.
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