p-integral bases of algebraic number fields - Alaca, Şaban (Utilitas Mathematica, 1999)
Let K be an algebraic number field of degree n, let p be a rational prime, and let α ∈ K. If νP (α) ≥ 0 for each prime ideal P of K such that P\pOK then α is called a p-integral element of K. Let {w1, w2,..., wn} be a basis of K over Q, where each wi (1 ≤ i ≤ n) is a p-integral element of K. If every p-integral element α of K is given as α = a1w1 + a2w2 + ⋯ + anwn, where the ai are p-integral elements of Q, then {w1, w2,..., wn} is called a p-integral basis of K. The properties of p-integral bases of an algebraic number field K are developed, and used to show how an integral basis of K can be obtained from its p-integral bases.