Localization (commutative algebra): Difference between revisions

Revision as of 21:16, 30 January 2022

Revision as of 01:03, 3 March 2022

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is an isomorphism. If <math>M</math> is a [[finitely presented module]], the natural map

:<math>S^{-1} \operatorname{Hom}_R (M, N) \to \operatorname{Hom}_{S^{-1}R} (S^{-1}M, S^{-1}N)</math>

is also an isomorphism.<ref>{{citation neededharvnb|Eisenbud|dateloc=MarchProposition 20212.10}}</ref>

If a module ''M'' is a [[finitely generated module|finitely generated]] over ''R'', one has