localization

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EnglishEdit

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EtymologyEdit

From localize +‎ -ation; compare French localisation.

NounEdit

localization (countable and uncountable, plural localizations)

  1. The act of localizing.
    1. (software engineering) The act or process of making a product suitable for use in a particular country or region.
  2. The state of being localized.
  3. (algebra) A systematic method of adding multiplicative inverses to a ring.
  4. (algebra) A ring of fractions of a given ring, such that the complement of the set of allowed denominators is an ideal.
    • 2007, Ivan Fesenko, “Rings and modules”, in G13ALS Algebra 2, 2007/2008 @ maths.nottingham.ac.uk[1], page 27:
         3) Geometric interpretation of the localization.
         Let V be an irreducible algebraic variety. Then P = J(V) is a prime ideal of   and so   is an integral domain.
         The localization   is a subring of   consisting of rational functions   which are defined on a nonempty subset of V. If V = {x} is a point, then P is maximal and   consists of rational functions which are defined at x.

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