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Nontrivial Galois module structure of cyclotomic fields | | Marc Conrad
; Daniel R. Replogle
; | | Date: |
17 Dec 2001 | | Subject: | Number Theory | math.NT | | Abstract: | We say a tame Galois field extension $L/K$ with Galois group $G$ has trivial Galois module structure if the rings of integers have the property that $Cal{O}_{L}$ is a free $Cal{O}_{K}[G]$-module. The work of Greither, Replogle, Rubin, and Srivastav shows that for each algebraic number field other than the rational numbers there will exist infinitely many primes $l$ so that for each there is a tame Galois field extension of degree $l$ so that $L/K$ has nontrivial Galois module structure. However, the proof does not directly yield specific primes $l$ for a given algebraic number field $K.$ For $K$ any cyclotomic field we find an explicit $l$ so that there is a tame degree $l$ extension $L/K$ with nontrivial Galois module structure. | | Source: | arXiv, math.NT/0201322 | | Services: | Forum | Review | PDF | Favorites | |
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