Quadratic and Cyclotomic Fields
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  as well as the classical treatise by H. Smith .
KeywordsPrime Ideal Galois Group Number Field Class Number Fundamental Unit
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