Alg Flashcards
(68 cards)
1
Q
standard sets
A
1
Z,Q,R,C,M_{mxn}(S), M_n(S)”+” superscript, “+” with overbar, *
2
Q
binary operation on S
A
2
3
Q
closed under an operation
A
3
4
Q
associative
A
4
5
Q
semigroup
A
5
6
Q
identity
A
6
7
Q
monoid
A
7
8
Q
inverse
A
8
9
Q
group
A
9
defn, equivalently 4 conditions
10
Q
properties of groups
A
10
6 of em
11
Q
commutative
A
11
12
Q
Abelian
A
12
13
Q
order of S
A
13
14
Q
examples of groups
A
14
7 groups, 2 more
15
Q
general linear group
A
15
16
Q
special linear group
A
16
17
Q
nth roots of unity
A
17
18
Q
symmetric group on n letters
A
18
19
Q
dihedral group
A
19
20
Q
group table
A
20
21
Q
additive group of integers modulo n
A
21
22
Q
multiplicative group of integers modulo p
A
22
23
Q
cyclic group
A
23
24
Q
generator of (Z_n,+)
A
24
25
when a^m is a generator of G
25
26
subgroup
26
27
center
27
28
cyclic subgroup generated by a
28
29
order of an element
29
30
finitely generated group
30
31
relations
31
| defn, Klein four-group presentation
32
Lagrange's theorem
32
33
Abelian subgroup of certain order
33
34
subgroups of cyclic groups
34
35
Cauchy's theorem
35
36
Sylow's first theorem
36
37
isomorphic
37
38
direct product
38
39
when Z_m+Z_n+... is cyclic
39
40
elementary divisors of G
40
41
invariant factors of G
41
42
coset
42
43
group homomorphism
43
44
monomorphism
44
45
epimorphism
45
46
isomorphism
46
47
endomorphism
47
48
automorphism
48
49
properties of homomorphisms
49
| 6 of em
50
kernel
50
51
ring
51
| 3 main conditions, total of 8 sub-conditions
52
ring with unity
52
53
commutative ring
53
54
subring
54
55
characteristic of the ring
55
56
ring of integers
56
57
ring of integers modulo n
57
58
ring of Gaussian integers
58
59
ring of real-valued functions on R
59
60
ring homomorphism
60
61
properties of ring homomorphism
61
| 3 of em
62
integral domain
62
63
zero divisor
63
64
zero divisors in Z_n
64
65
integral domains Z_n
65
66
unit
66
67
division ring
67
68
field
68
| defn, 6 conditions
