Hilbert 90 for biquadratic extensions

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Hilbert's Theorem 90 is a classical result in the theory of cyclic extensions. The quadratic case of Hilbert 90, however, generalizes in noncyclic directions as well. Informed by a poem of Richard Wilbur, the article explores several generalizations, discerning connections among multiplicative groups of fields, values of binary quadratic forms, a bit of module theory over group rings, and even Galois cohomology.
v2 (15 pages); followed Monthly style sheet and added additional exposition

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Number Theory, Rings and Algebras, 12F10; 12G05

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http://salesiana.dossiersoluciones.com/handle/123456789/163628

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0510154
 http://arxiv.org/abs/math/0510154
 Amer. Math. Monthly 114 (2007), no. 7, 577--587

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arXiv