This chapter achieves two purposes simultaneously. It gives examples for the theory, and also describes in greater details the cyclotomic fields which exert a great deal of control over algebraic number theory in general. The extent to which they exert this control is in fact not yet clearly understood, but one knows for instance that the heart of the proofs of class field theory is concentrated in the cyclotomic fields.
KeywordsFinite Field Galois Group Prime Power Residue Class Algebraic Integer
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