Graduate Thesis Or Dissertation

 

Euclid's Algorithm in Multiquadratic Fields Public Deposited

https://scholar.colorado.edu/concern/graduate_thesis_or_dissertations/05741r744
Abstract
  • In this thesis we find that all imaginary n-quadratic fields with n>3 have class number larger than 1 and therefore cannot be Euclidean. We also examine imaginary triquadratic fields, presenting a complete list of 17 imaginary triquadratic fields with class number 1, and classifing many of them according to whether or not they are norm-Euclidean. We find that at least three of these fields are norm-Euclidean, and at least five are not.
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  • 2014
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  • 2019-11-16
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