Cyclic algebras, Schur indices, norms, and Galois modules

Details Cyclic algebras, Schur indices, norms, and Galois modules Cyclic algebras, Schur indices, norms, and Galois modules

2004-10-25

arxiv.org/abs/math/0410536v2

Ann. Sci. Math. Quebec 35 (2011), no. 1, 123--136

Mathematics

Number Theory

v2 (16 pages); to appear in Annales des sciences mathematiques du Quebec

Scientific paper

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 F_pG-module K^*/K^{*p} of pth-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<=i

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