The ring of integers of a number field

Question 1

ring of integers

Answer 1

set of all algebraic integers in K

Question 2

Gram matrix A

Answer 2

entries: <ai,aj> =Tr(aiaj)

Question 3

discriminant

Answer 3

detA

Question 4

integral basis

Answer 4

if ai is Q basis and every β in I may be written as βiαi where βi are in Z

Question 5

Δ(I)

Answer 5

of any integral basis of I

Question 6

Δ(K)

Answer 6

Δ(OK)