Unique Factorisation of Ideals Flashcards
1
Q
norm of ideal
A
size of quotient ring O_K/I
2
Q
Ascending Chain Condition
A
In O_K every chain of ideals stabilises
3
Q
sum of ideals
A
a+b, a in I, b in J
4
Q
product of ideals
A
sum of I of a_i b_i
5
Q
prime ideal
A
I is proper and if ab in I, then a in I or b in I
6
Q
maximal ideal
A
I proper and there is no ideal J strictly between I and R
7
Q
cancellation law
A
if IJ_1=IJ_2 then J_1=J_2
8
Q
“to contain is to divide”
A
If I_1<I_2 then there exists J st I_1=I_2J
