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Flashcards in AlegraQual_entire Deck (100):
1

group + 5 properties, abelain, examples

1

2

Sn, An, Dn

2

3

subgroup, subgroup generated by S

3

4

homomorphism, monomorphism, epimorphism, isomorphism

4

5

equivalence relation

5

6

cosets

6

7

Lagranges Theorem (+ 2 corollaries)

7

8

index

8

9

completely classify ≤g>

9

10

normal subgroup + Theorem

10

11

conjugation

11

12

simple

12

13

Theorem (coset representations)

13

14

First Isomorphism Theorem

14

15

center

15

16

4 propositions for normalchange to combine 1 and 2!!

16

17

2nd and 3rd isomorphism Theorems

17

18

Direct product

18

19

free group + normal closure + free abelian group

19

20

action + faithful + kernel + stabilizer

20

21

equivalence classes of an orbit + transitive + free + Theorem + Theorem

21

22

center + stabilizer + centralizer + normalizer

22

23

free abelian group generated by S

23

24

Fundamental Theorem on finitely generated abelian groups

24

25

p-group + Theorem + Corollary + Proposition

25

26

1st Sylow Theorem

26

27

Sylow p-subgroups

27

28

2nd Sylow Theorem

28

29

3rd Sylow Theorem

29

30

groups of each order

30

31

ring

31

32

(left) zero divisor + left invertible

32

33

integral domain + division ring + field + homomorphism

33

34

(left) ideal

34

35

principal ideal + principal ring + PID

35

36

Theorems about ideals (3) + ex

36

37

prime ideal + Theorem + Theorem

37

38

maximal + theorems (3)

38

39

Theorem (direct product, ideals) + Corollary + Corollary

39

40

divides + Proposition + Corollary + Proposition

40

41

irreducible element + Prop + prime element + Thrm

41

42

Chinese Remainder Theorem

42

43

UFD, Noetherian

43

44

Euclidean, Prop

44

45

ring of quotients, localization of R at P

45

46

Theorem (S^{-1}R), Corollary

46

47

local

47

48

polynomials over R, Properties (3), Theorem

48

49

ring of formal power series, Proposition

49

50

Bezout’s Theorem, Prop, Prop

50

51

content, Lemma

51

52

Theorem (name???)

52

53

Theorem (???)

53

54

category, morphism, isomorphism

54

55

covariant / contravariant functor

55

56

module, ex, _RM

56

57

quotient modules

57

58

R-module homomorphism, Theorem (TFAE 4)

58

59

First Isomorphism Theorem

59

60

direct product (external/internal) direct sum

60

61

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

61

62

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

62

63

additive functor, exact

63

64

left/right exact

64

65

sub-R-module generated by S, finitely generated, linearly in

65

66

torsion

66

67

Splitting Lemma, Proposition

67

68

projective defn, Theorem, Corollary

68

69

injective defn, Theorem

69

70

divisible abelian group, proposition

70

71

tensor product, Theorem, Note

71

72

tensor product examples (x4), Prop, Prop, Prop

72

73

Theorem (F_M : _RM -> Ab), Theorem, Cor, Cor

73

74

(S,R)-bimodule

74

75

invariant dimension property, theorem, proposition

75

76

flat, proposition (3)

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77

Noetherian (3), Proposition, Coroallry, Proposition

77

78

Hilberts Basis Theroem

78

79

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

79

80

Elementary divisors theorem

80

81

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

81

82

extension, alpha algebraic, algebraic, dimension, K(alpha),

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83

quotient by function theorem

83

84

rho, irreducible polynomial of an algebraic element, Proposi

84

85

compositum of fields

85

86

prime field

86

87

Great Theorem about field extensions (6)

87

88

algebraically closed, 2x ex, Theorem, Lemma, Theorem, Coroll

88

89

embedding, key fact

89

90

splitting field of f, Proposition, Proposition

90

91

embedding, Emb, f^sigma

91

92

Lifting Lemma, Corollary, ex

92

93

splitting field, Theorem (2)

93

94

normal extension definition (3), Theorem (4)

94

95

Lemma, separable extension, Theorem, defn, Lemma, Theorem, T

95

96

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

96

97

perfect, Frobenius map, Proposition

97

98

Galois extension, Proposition 1, Proposition 2, Proposition

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99

positive element theorem

99

100

Fundamental Theorem of Galois Theory

100