ABSTRACT
A key concept in number theory is that of an algebraic integer. It emerged through the work of Gauss, Dirichlet, Eisenstein, Kummer, Kronecker, Hilbert, and others. It is a generalization of the notion of (usual) integer; and many theorems about algebraic integers have, as consequences, theorems about the usual integers. A typical example of this will be the proof of the Quadratic Reciprocity Law of Gauss.
