Published online by Cambridge University Press: 24 October 2008
Let p be a prime number, and let K be a finite extension of the rational p-adic field ℚp. Let L/K be a finite abelian extension with Galois group G, and let L,
K denote the valuation rings of L, K respectively. Then L is a free module of rank 1 over the group algebra KG. Defining the associated order
of the extension L/K by
L can be viewed as a module over the ring
, and a fortiori over the group ring
KG.