Mathematical Journal of Okayama University volume61 issue1
2019-01 発行

The Factorization of 2 and 3 in Cyclic Quartic Fields

Brown, Stephen C. Department of Computer Science, Mathematics, Physics and Statistics I.K. Barber School of Arts and Sciences University of British Columbia
Davis, Chad T. Department of Computer Science, Mathematics, Physics and Statistics I.K. Barber School of Arts and Sciences University of British Columbia
Publication Date
2019-01
Abstract
Due to a theorem of Dedekind, factoring ideals generated by prime numbers in number fields is easily done given that said prime number does not divide the index of the field. In this paper, we determine the prime ideal factorizations of both 2 and 3 in cyclic quartic fields whose index is divisible by one of or both of these primes.
Keywords
Cyclic quartic field
Prime ideal factorization
Comments
Mathematics Subject Classification. Primary 11R16; Secondary 11R27.