Gruppendeterminante und K�rperdiskriminante

Speiser, Ambros P.

doi:10.1007/bf01456968

Cited by 19 publications

(5 citation statements)

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“…Namely, since all the ideals of kp are principal, the ideal α of kp is generated by an element a of kp, hence if A runs over all the elements of 91, then a A also runs over all the elements of the ideal α 9ί. Therefore, our assertion follows at once from [3], E. Noether [4]).…”

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confidence: 60%

On the Ring of Integers in an Algebraic Number Field as a representation Module of Galois Group

Yokoi¹

1960

Nagoya Mathematical Journal

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1. Introduction. It is known that there are only three rationally inequivalent classes of indecomposable integral representations of a cyclic group of prime order l. The representations of these classes are: (I) identical representation,(II) rationally irreducible representation of degree l – 1,(III) indecomposable representation consisting of one identical representation and one rationally irreducible representation of degree l-1 (F. E. Diederichsen [1], I. Reiner [2]).

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confidence: 60%

On the Ring of Integers in an Algebraic Number Field as a representation Module of Galois Group

Yokoi¹

1960

Nagoya Mathematical Journal

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“…Therefore, Theorem 1.1 implies the following criterion which is usually known as Noether's criterion, part of which goes back to Speiser [146] (he proved the necessary condition), and which is presented as the basic starting point of Galois module structure theory:…”

Section: Classical Galois Module Theory For Number Fieldsmentioning

confidence: 99%

On the Galois module structure of extensions of local fields

Thomas¹

2010

Publications Mathématiques De Besançon

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“…mp*) is the conductor for K real (resp. imaginary), and KQQ{m) 9 the cyclotomic field of m-th roots of unity over the rationals. If K/Q is tamely ramified, then m = l x l r9 a product of distinct odd primes.…”

Section: Definition An Ideal 21 Of K Has An 0 F G-normal Basis If 21mentioning

confidence: 99%

“…Let KjF be a Galois extension of number fields. A necessary condition that O^ have a normal basis was given by Speiser [9], namely that KjF be tamely ramified. Hubert [4,Theorem 132] showed O# has a normal basis when K\Q is abelian and the degree of K/Q is prime to the discriminant of KIQ.…”

Section: Introductionmentioning

confidence: 99%

Normal Bases in Galois Extensions of Number Fields

Ullom

1969

Nagoya Mathematical Journal

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The notion of module together with many other concepts in abstract algebra we owe to Dedekind [2]. He recognized that the ring of integers OK of a number field was a free Z-module. When the extension K/F is Galois, it is known that K has an algebraic normal basis over F. A fractional ideal of K is a Galois module if and only if it is an ambiguous ideal. Hilbert [4, §§105-112] used the existence of a normal basis for certain rings of integers to develop the theory of root numbers — their decomposition already having been studied by Kummer.

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Gruppendeterminante und K�rperdiskriminante

Cited by 19 publications

References 2 publications

On the Ring of Integers in an Algebraic Number Field as a representation Module of Galois Group

On the Ring of Integers in an Algebraic Number Field as a representation Module of Galois Group

On the Galois module structure of extensions of local fields

Normal Bases in Galois Extensions of Number Fields

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