Number fields

Question 1

algebraic number

Answer 1

root of a non-zero polynomial with rational coefficients

Question 2

algebraic integer

Answer 2

root of monic polynomial with integer coefficients

Question 3

minimal polynomial

Answer 3

monic polynomial with lowest degree such that a is a root

Question 4

degree of K

Answer 4

dimension as a Q-vector space

Question 5

number field

Answer 5

subfield of C with finite degree over Q

Question 6

quadratic field

Answer 6

number field of degree 2

Question 7

cubic field

Answer 7

degree 3

Question 8

cyclotomic field

Answer 8

generated by a root of unity

Question 9

trace of a

Answer 9

trLa

Question 10

norm of a

Answer 10

detLa