Jan Minac, Andrew Schultz, John Swallow: Cyclic algebras and construction of some Galois modules

minac@uwo.ca, aschultz@stanford.edu, joswallow@davidson.edu

Submission: 2004, Oct 30

Let $p$ be a prime and suppose that $K/F$ is a cyclic extension of degree $p^n$ with group $G$. Let $J$ be the $\mathbb{F}_p G$-module $K^\times/K^{\times p}$ of $p$th-power classes. In our previous paper we established precise conditions for $J$ to contain an indecomposable direct summand of dimension not a power of $p$. At most one such summand exists, and its dimension must be $p^i+1$ for some $0\le i

2000 Mathematics Subject Classification: 12F10, 16K50

Keywords and Phrases: cyclic algebras, Galois modules, index, roots of unity

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