Geodesic
Elementary Generalizations of Hilbert's Theorem 90
Canadian mathematical bulletin, Tome 8 (1965) no. 6, pp. 749-757

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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 
Connell, Ian G. Elementary Generalizations of Hilbert's Theorem 90. Canadian mathematical bulletin, Tome 8 (1965) no. 6, pp. 749-757. doi: 10.4153/CMB-1965-055-2
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     author = {Connell, Ian G.},
     title = {Elementary {Generalizations} of {Hilbert's} {Theorem} 90},
     journal = {Canadian mathematical bulletin},
     pages = {749--757},
     year = {1965},
     volume = {8},
     number = {6},
     doi = {10.4153/CMB-1965-055-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1965-055-2/}
}
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