http://www1.spms.ntu.edu.sg/~frederique/antchap1.pdfChapter 1 Algebraic Numbers and Algebraic Integers 1.1 Rings of integers We start by introducing two essential notions: number field and algebraic inte- ger. Definition 1.1. A number field is a finite field extension K of Q, i.e., a field which is a Q-vector space of finite dimension. We note this dimension [K : Q] and call it the degree of K. Examples 1.1. 1. The field Q( √ 2) = {x + y √ 2 | x, y
