Algebra II

Question 1

category, morphism, isomorphism

Answer 1

1

Question 2

covariant / contravariant functor

Answer 2

2

Question 3

module, ex, _R\M

Answer 3

3

Question 4

quotient modules

Answer 4

4

Question 5

R-module homomorphism, Theorem (TFAE 4)

Answer 5

5

Question 6

First Isomorphism Theorem

Answer 6

6

Question 7

direct product (external/internal) direct sum

Answer 7

7

Question 8

exact sequences, Proposition (0) , Proposition (0), short exact sequence

Answer 8

8

Question 9

Hom_R(A,B), Proposition, Hom_R(M,-), Proposition, Theorem

Answer 9

9

Question 10

additive functor, exact

Answer 10

10

Question 11

left/right exact

Answer 11

11

Question 12

sub-R-module generated by S, finitely generated, linearly independent, basis, free, Proposition, Corollary

Answer 12

12

Question 13

torsion

Answer 13

13

Question 14

Splitting Lemma, Proposition

Answer 14

14

Question 15

projective defn, Theorem, Corollary

Answer 15

15

Question 16

injective defn, Theorem

Answer 16

16

Question 17

divisible abelian group, proposition

Answer 17

17

Question 18

tensor product, Theorem, Note

Answer 18

18

Question 19

tensor product examples (x4), Theorem, Corollary, Corollary

Answer 19

19

Question 20

Theorem (F_M : _R\M -> Ab)

Answer 20

20

Question 21

(S,R)-bimodule, Proposition (x4)

Answer 21

21