XI. Modules

Question 1

Theorem X.6.5
Every P.I.D. is a …

Question 2

Definition
R-module.

Question 3

Definition
R-submodule.

Question 4

Definition
Quotient module.

Question 5

Lemma XI.2.6
Direct product is…

Question 6

Definition
Module homomorphism.
Isomorphism.

Question 7

Theorem XI.2.10
The Isomorphism Theorem.

Question 8

Exercise XI.2.11
\phi is injective iff.

Question 9

Exercise XI.2.12
The Correspondence Theorem

Question 10

Definition
R-span.
Spans/generated.
Finitely generated.

Question 11

Exercise XI.3.1
Span_{R}(x) is a…

Question 12

Exercise XI.3.2
R^{n} is…

Question 13

Theorem XI.3.3
M is finitely generated iff.

Question 14

Definition
R-linearly independent.
R-basis.
Free of rank n.

Question 15

Exercise X1.3.4
A subset is an R-basis iff.

Question 16

Theorem XI.4.1
Fundamental Theorem of Finitely-generated Abelian Modules over Euclidean Rings

Question 17

Definition
Invariants.
Rank.

Question 18

Theorem XI.4.2
Fundamental Theorem of Finitely-generated Abelian Groups.

Question 19

Exercise XI.4.5
n is a square free positive integer…

Question 20

Theorem XI.5.1
If F a field and G a finite subgroup…

Question 21

Theorem XI.6.1
If N is an R-submodule of P.I.D., span

Question 22

Corollary XI.6.2
If N is an R-submodule of P.I.D., matrix

Question 23

Theorem XI.7.1
Smith Normal form.

Question 24

Lemma XI.7.2
Let C=UA, then

Question 25

Lemma XI.7.3
Let B=UAV, then…

Question 26

Definition
Elementary matrices.