Hilbert 90 for Biquadratic Extensions

Author

Roman Dwilewicz, Missouri University of Science and TechnologyFollow
Jan Minac
Andrew Schultz
John Swallow

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.

Recommended Citation

R. Dwilewicz et al., "Hilbert 90 for Biquadratic Extensions," The American Mathematical Monthly, Mathematical Association of America (MAA), Jul 2006.

Department(s)

Mathematics and Statistics

Sponsor(s)

Natural Sciences and Engineering Research Council of Canada
Polish Committee for Scientific Research
University of Missouri Research Board

Keywords and Phrases

Hilbert's Theorem 90; cyclic extensions; noncyclic directions

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2006 Mathematical Association of America (MAA), All rights reserved.

Publication Date

01 Jul 2006