Algebra II - final

Question 1

invariant dimension property, theorem, proposition

Answer 1

22

Question 2

flat, proposition (3)

Answer 2

23

Question 3

Noetherian (3), Proposition, Coroallry, Proposition

Answer 3

24

Question 4

Hilbert’s Basis Theroem

Answer 4

25

Question 5

torsion-free, Lemma, Theorem 1, Theorem 2, Theorem 3 (3)

Answer 5

26

Question 6

Elementary divisors theorem

Answer 6

27

Question 7

K[x], division algorithm, corollary (2)

Answer 7

28

Question 8

extension, alpha algebraic, algebraic, dimension, K(alpha), Lemma (2x2)

Answer 8

29

Question 9

quotient by function theorem

Answer 9

30

Question 10

rho, irreducible polynomial of an algebraic element, Proposition, Corollary, Proposition, Proposition

Answer 10

31

Question 11

compositum of fields

Answer 11

32

Question 12

prime field

Answer 12

33

Question 13

Great Theorem about field extensions (6)

Answer 13

34

Question 14

algebraically closed, 2x ex, Theorem, Lemma, Theorem, Corollary, Proposition

Answer 14

35

Question 15

embedding, key fact

Answer 15

36

Question 16

splitting field of f, Proposition, Proposition

Answer 16

37

Question 17

embedding, Emb, f^sigma

Answer 17

38

Question 18

Lifting Lemma, Corollary, ex

Answer 18

39

Question 19

splitting field, Theorem (2)

Answer 19

40

Question 20

normal extension definition (3), Theorem (4)

Answer 20

41

Question 21

Lemma, separable extension, Theorem, defn, Lemma, Theorem, Theorem, Proposition

Answer 21

42

Question 22

inseparable defn (4), Proposition about mu (3), corollary (3)

Answer 22

43

Question 23

perfect, Frobenius map, Proposition

Answer 23

44

Question 24

Galois extension, Proposition 1, Proposition 2, Proposition 3

Answer 24

45

Question 25

positive element theorem

Answer 25

46

Question 26

Fundamental Theorem of Galois Theory

Answer 26

47