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.