Excerpt from The Elements of the Theory of Algebraic Numbers
It has been my endeavor in this book to lead by easy stages a reader, entirely unacquainted with the subject, to an appreciation of some of the fundamental conceptions in the general theory of algebraic numbers. With this object in view, I have treated the theory of rational integers more in the manner of the general theory than is usual, and have emphasized those properties of these integers which find their analogues in the general theory. The same may be said of the general quadratic realm, which has been treated rather as an example of the general realm of the nth degree than simply as of the second degree, as little use as was possible, without too great sacrifice of simplicity, being made of the special properties of the quadratic realm in the proofs. The theorems and their proofs have therefore been so formulated as to be readily extendable, in most cases, to the general realm of the nth degree, and it is hoped that a student, who wishes to continue the study of the subject, will find the reading of works on the general theory, such as Hilbert's Bericht uber die Theorie der Algebraischen Zahlkorper, rendered easier thereby. The proofs of the theorems relating to biquadratic residues have necessarily been omitted but the examples given will make the reader acquainted with their content.
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