Commutative algebra - Department of Mathematical Sciences - old ...
Commutative algebra - Department of Mathematical Sciences - old ...
Commutative algebra - Department of Mathematical Sciences - old ...
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projections, 28<br />
projective module, 50<br />
projective modules, 50<br />
proper ideal, 11<br />
radical, 14<br />
rank, 76<br />
reduced, 14<br />
reduced primary decomposition, 106<br />
reflexive module, 33<br />
residue field, 67<br />
residue homomorphism, 68<br />
restriction <strong>of</strong> scalars, 22<br />
retraction, 41<br />
ring, 9<br />
ring extension, 9<br />
ring generated, 17<br />
ring <strong>of</strong> fractions, 57<br />
rings, 9<br />
rings <strong>of</strong> fractions, 57<br />
root, 18<br />
roots, 18<br />
scalar multiplication, 21, 22<br />
section, 41<br />
short exact sequence, 40<br />
simple module, 85<br />
simple modules, 85<br />
simple root, 18<br />
snake homomorphism, 44<br />
snake lemma, 45<br />
spectrum, 101<br />
split exact sequence, 42<br />
standard basis, 29<br />
subfield, 19<br />
subgroup, 9<br />
submodule, 21<br />
submodule generated, 23<br />
submodules and factor modules, 23<br />
subring, 9<br />
sum and product, 28<br />
support, 101<br />
support <strong>of</strong> modules, 101<br />
symbolic power, 108<br />
tensor modules <strong>of</strong> fractions, 62<br />
tensor product, 33<br />
tensor product modules, 33<br />
tensor product ring, 38<br />
the length, 85<br />
the polynomial ring is factorial, 64<br />
the snake lemma, 43<br />
torsion element, 111<br />
torsion free module, 111<br />
torsion submodule, 111<br />
total ring <strong>of</strong> fractions, 58<br />
uniformizing parameter, 112<br />
INDEX 121<br />
unique factorization, 15<br />
unique factorization domain, 15<br />
unit, 10<br />
valuation, 113<br />
vector space, 22<br />
windmill lemma, 46<br />
zero, 9<br />
zero divisor, 10, 22<br />
zero ideal, 11<br />
zero module, 21<br />
zero submodule, 21