Vol. 22, No. 2, 1967

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Irreducible integers in Galois extensions

Richard Thomas Bumby

Vol. 22 (1967), No. 2, 221–229

We start from the question: When are the irreducible integers of a number field determined by their norms? Attention is centered on the case in which the word “norm” is taken to mean the relative norm of a Galois extension. In this case we are able to show that the ideal class group, as a module over the Galois group, is severely limited by this condition. The restriction of this question to (relatively) quadratic extensions has special properties which are studied in further detail. The homological methods which are in the background of our study become very useful in the study of quadratic extensions.

Mathematical Subject Classification
Primary: 10.65
Secondary: 12.00
Received: 22 August 1966
Published: 1 August 1967
Richard Thomas Bumby