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Changing short description from "Construction of a ring of fractions, in commutative algebra" to "Construction of a ring of fractions" (Shortdesc helper) |
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In [[commutative algebra]] and [[algebraic geometry]], '''localization''' is a formal way to introduce the "denominators" to a given [[ring (mathematics)|ring]] or [[module (mathematics)|module]]. That is, it introduces a new ring/module out of an existing ring/module ''R'', so that it consists of [[algebraic fraction|fractions]] <math>\frac{m}{s},</math> such that the [[denominator]] ''s'' belongs to a given subset ''S'' of ''R''. If ''S'' is the set of the non-zero elements of an [[integral ___domain]], then the localization is the [[field of fractions]]: this case generalizes the construction of the ring <math>\Q</math> of [[rational number]]s from the ring <math>\Z</math> of [[integer]]s.
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