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Elementary Generalizations of Hilbert's Theorem 90

Published online by Cambridge University Press:  20 November 2018

Ian G. Connell
Ian G. Connell*
Affiliation:
McGill University
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Let K, k be fields and K|k a finite galois extension with galois group G. The multiplicative group K* of K is a G-module, that is, a module over the integral group ring ZG, the module action of an element σ ϵ G being its effect as an automorphism. It is shown in [2, p. 158] that the first cohomology group vanishes:

1

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 8 , Issue 6 , December 1965 , pp. 749 - 757
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Gruenberg, K. W., Resolutions by Relations, London Math. Soc. J., vol.35(1960), pp. 481-494.Google Scholar
2. Serre, J. P., Corps Locaux, Paris, 1962.Google Scholar