Page "Algebraic number" Paragraph 23

The sum, difference and product of algebraic integers are again algebraic integers, which means that the algebraic integers form a ring.

The name algebraic integer comes from the fact that the only rational numbers which are algebraic integers are the integers, and because the algebraic integers in any number field are in many ways analogous to the integers.

If K is a number field, its ring of integers is the subring of algebraic integers in K, and is frequently denoted as O < sub > K </ sub >.