English

Hilbert 90 for biquadratic extensions

Number Theory 2008-06-26 v3 Rings and Algebras

Abstract

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.

Keywords

Cite

@article{arxiv.math/0510154,
  title  = {Hilbert 90 for biquadratic extensions},
  author = {Roman Dwilewicz and Jan Minac and Andrew Schultz and John Swallow},
  journal= {arXiv preprint arXiv:math/0510154},
  year   = {2008}
}

Comments

v2 (15 pages); followed Monthly style sheet and added additional exposition