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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The annihilator of radical powers in the modular group ring of a $p$-group
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by E. T. Hill
Proc. Amer. Math. Soc. 25 (1970), 811-815
DOI: https://doi.org/10.1090/S0002-9939-1970-0262387-3

Abstract:

We show that if $N$ is the radical of the group ring and $L$ is the exponent of $N$, then the annihilator of ${N^w}$ is ${N^{L - w + 1}}$. As corollaries we show that the group ring has exactly one ideal of dimension one and if the group is cyclic, then the group ring has exactly one ideal of each dimension.
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Bibliographic Information
  • © Copyright 1970 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 25 (1970), 811-815
  • MSC: Primary 20.80
  • DOI: https://doi.org/10.1090/S0002-9939-1970-0262387-3
  • MathSciNet review: 0262387