Nontrivial Galois module structure of cyclotomic fields
نویسندگان
چکیده
منابع مشابه
Nontrivial Galois module structure of cyclotomic fields
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 OL is a free OK [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 extensio...
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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 OL is a free OK [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 extensio...
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Let K be an algebraic number field with ring of integers OK , p > 2, be a rational prime and G the cyclic group of order p. Let Λ denote the order OK [G]. Let Cl(Λ) denote the locally free class group of Λ and D(Λ) the kernel group, the subgroup of Cl(Λ) consisting of classes that become trivial upon extension of scalars to the maximal order. If p is unramified in K, then D(Λ) = T (Λ), where T ...
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Let k0 be a finite algebraic number field in a fixed algebraic closure Ω and ζn denote a primitive n-th root of unity ( n ≥ 1). Let k∞ be the maximal cyclotomic extension of k0, i.e. the field obtained by adjoining to k0 all ζn ( n = 1, 2, ...). Let M and L be the maximal abelian extension of k∞ and the maximal unramified abelian extension of k∞ respectively. The Galois groups Gal(M/k∞) and Gal...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2002
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-02-01457-6