X. Principal Ideal Domains Flashcards
1
Q
Definition
Ideal of ring.
A
2
Q
Lemma X.1.1
An ideal I = R iff.
A
3
Q
Definition
Sum of ideals.
Product of ideals.
A
4
Q
Lemma X.1.2
Properties of ideals.
A
5
Q
Definition
Set of multiples.
A
6
Q
Lemma X.1.3
a \in R, then Ra is…
A
7
Q
Definition
Principal ideal generated by…
Principal.
A
8
Q
Definition
Ideal generated by…
A
9
Q
Lemma X.2.1
equivalences to b \in Ra
A
10
Q
Lemma X.2.2
Ra = Rb iff.
Ra = R iff.
A
11
Q
Definition
Principle Ideal Domain
A
12
Q
Theorem X.4.1
If R is a Euclidean domain…
A
13
Q
Corollary X.4.4
For any field K, K[x] is…
A
14
Q
Theorem X.5.1
In a P.I.D., the primes of R are…
A
15
Q
Lemma X.5.3
In a P.I.D. unique factorisation…
A
