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Proceedings of the American Mathematical Society

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

 

 

Ideals in the modular group ring of a $ p$-group


Author: E. T. Hill
Journal: Proc. Amer. Math. Soc. 28 (1971), 389-390
MSC: Primary 20.80
DOI: https://doi.org/10.1090/S0002-9939-1971-0276373-1
MathSciNet review: 0276373
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Abstract: We show that if $ G$ has order $ {p^n}$ then the group ring has a chain of $ {p^n} + 1$ ideals and that the radical powers are canonical in the lattice of ideals. We then prove that if $ G$ is abelian, $ G$ is determined by the lattice of ideals.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0276373-1
Keywords: Modular group ring, lattice of ideals
Article copyright: © Copyright 1971 American Mathematical Society