Hilbert 90 for Biquadratic Extensions
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.
R. Dwilewicz et al., "Hilbert 90 for Biquadratic Extensions," The American Mathematical Monthly, Mathematical Association of America (MAA), Jul 2006.
Mathematics and Statistics
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
Article - Journal
© 2006 Mathematical Association of America (MAA), All rights reserved.