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Atrium > Mathematics, Physics & Philosophy: relation between completion and localization

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    • CommentRowNumber1.
    • CommentAuthorelif
    • CommentTimeJun 8th 2014
    How can we proof existence of isomorphism between completion of the localization at maximal ideal and completion at maximal ideal? Why this relation is not true when we take any ideal?
    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeJun 9th 2014

    It does not make sense to talk about commutative localization at an arbitrary ideal. The “localization at ideal” is in fact localization at its complement, i.e. we inverse the complement set. This complement must be a multiplicative set, what (in commutative case) means that the ideal is prime. So, this is just a little more general (and more natural) than maximal.

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