Algebraic Numbers, The Algebraic Integers are Dedekind

The Algebraic Integers are Dedekind

A global field is a finite separable extension, and the base ring, either Z or Zp[t], is a pid. Apply a general theorem describing the ring of integers over a dedekind domain, and the algebraic integers become dedekind. It's practically a corollary.

In addition, the algebraic integers form a free R module of rank n, where R is the base ring. We can describe the integral ring as the span of a basis b1 through bn.