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The main results of this paper may be loosely stated as follows.Theorem.— Let $N$ and $N^{'}$ be sums of Galois algebras with group $Γ$ over algebraic number fields. Suppose that $N$ and $N^{'}$ have the same dimension $ℚ$ and that they are identical at their wildly ramified primes. Then (writing $𝒪_{N}$ for the maximal order in $N$ ) $𝒪_{N} \oplus 𝒪_{N} \oplus ℤ Γ ≅_{ℤ Γ} \oplus 𝒪_{N}^{'} \oplus 𝒪_{N^{'}} \oplus ℤ Γ .$ In many cases $𝒪_{N} ≅_{ℤ Γ} 𝒪_{N^{'}} .$ The role played by the root numbers of $N$ and $N^{'}$ at the symplectic characters of $Γ$ in determining the relationship between the $ℤ Γ$ -modules $𝒪_{N}$ and $𝒪_{N^{'}}$ is described. The theorem includes...

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Galois groups of exponent two and the Brumer-Stark conjecture.

Galois module structure in weakly ramified 3-extensions

Galois module structure of abelian extensions.

Galois module structure of integers of relative abelian extensions.

Galois module structure of Kummer orders and elliptic units.

Galois Module Structure of Rings of Intergers.

Galois module structure of the rings of integers in wildly ramified extensions

Galois modules and embedding problems.

Galois structure of de Rham cohomology

Galois-Cohen-Lenstra heuristics

Group laws and rings with normal bases.

Currently displaying 1 – 11 of 11