Abstract
In the last chapter we discussed the general theory of algebraic number fields and their rings of integers. We now consider in greater detail two important classes of these fields which were studied first in the nineteenth century by Gauss, Eisenstein, Kummer, Dirichlet, and others in connection with the theory of quadratic forms, higher reciprocity laws and Fermat’s Last Theorem. The reader who is interested in the historical development of this subject should consult the book by H. Edwards [128] as well as the classical treatise by H. Smith [72].KeywordsPrime IdealGalois GroupNumber FieldClass NumberFundamental UnitThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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