localization

Etymology

From localize + -ation; compare French localisation.

noun

1. The act of localizing.
   1. (HK politics, specifically) The switch of positions in power from the colonizing population to the local population.
      James has been responsible for the government works programme. He is the last expatriate senior official left in the administration, apart from the Attorney General, Jeremy Mathews. It has been a remarkably swift and comprehensive process of localization, and the competence of government in Hong Kong has not suffered an iota. His departure is a significant day for Hong Kong. 2022, Chris Patten, The Hong Kong Diaries, Penguin UK
2. (software engineering) The act, process, or result of making a product suitable for use in a particular country or region.
3. (translation studies, chiefly software, marketing) The act, process, or result of adapting translated text to fit a local culture; domestication.
4. The state of being localized.
5. (algebra) A systematic method of adding multiplicative inverses to a ring.
6. (algebra) A ring of fractions of a given ring, such that the complement of the set of allowed denominators is an ideal.
   3) Geometric interpretation of the localization. Let V be an irreducible algebraic variety. Then P = J(V) is a prime ideal of ℂ[X_1,...,X_n] and so ℂ[V]=ℂ[X_1,...,X_n]/J(V) is an integral domain. The localization ℂ[X_1,...,X_n]_P is a subring of ℂ(X_1,...,X_n) consisting of rational functions f/g:f,g∈ℂ[X_1,...,X_n],g∉P which are defined on a nonempty subset of V. If V = {x} is a point, then P is maximal and ℂ[X_1,...,X_n]_P=f/g:f,g∈ℂ[X_1,...,X_n],g(x) ne 0 consists of rational functions which are defined at x. 2007, Ivan Fesenko, “Rings and modules”, in G13ALS Algebra 2, 2007/2008 @ maths.nottingham.ac.uk, page 27