Hilbert 90 for biquadratic extensions
数论
2008-06-26 v3 环与代数
摘要
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.
引用
@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}
}
备注
v2 (15 pages); followed Monthly style sheet and added additional exposition