Commutative algebra - Department of Mathematical Sciences - old ...

A/B, 9
P -primary, 106
0-sequence, 39
abelian group, 9
addition, 9
annihilator, 27
artinian module, 87
artinian ring, 87
artinian rings, 87
ass of modules, 103
associated prime ideal, 103
associative, 9, 21
basis, 29
bilinear, 21
binomial formula, 10
canonical homomorphism, 59
canonical ring homomorphism, 57
Cayley-Hamilton’s theorem, 77
change of ring, 36
change of rings, 36
characteristic, 12
Chinese remainder theorem, 14
Chinese remainders, 14
coefficient, 16, 20
cofactor matrix, 75
cokernel, 25
colon ideal, 11, 27
comaximal ideals, 14
commutative, 9
composition series, 85
constants, 16
content of polynomial, 64
contracted ideal, 11
contravariant, 31
cosets, 9
Cramer’s rule, 76
decomposable, 30
decomposition of ideals, 108
decomposition of modules, 106
Dedekind domain, 113
Dedekind domains, 113
Index
119
degree, 16
derivative, 18
determinant, 75
direct product, 28
direct sum, 28, 29
discrete valuation ring, 112
discrete valuation ring of v, 113
discrete valuation rings, 112
distributive, 9
divisible module, 53
domain, 10
dual homomorphism, 33
dual module, 33
embedded prime, 105
essential extension, 54
evaluation, 32
evaluation map, 17
exact sequence, 39
exact sequences, 39
exactness and localization, 70
exactness of fractions, 60
exactness of hom, 48
exactness of tensor, 49
extended ideal, 11
factor group, 9
factor module, 24
factor ring, 11
faithfully flat, 71
faithfully flat ring homomorphism, 71
field, 10
field extension, 19
fields, 19
finite field extension, 19
finite ideal, 11
finite length, 85
finite module, 73
finite modules, 73
finite presented module, 80
finite presented modules, 80
finite ring extension, 83
finite ring homomorphism, 83
finite ring homomorphisms, 83
finite type ring, 17