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In commutative algebra and algebraic geometry, the localization is a formal way to introduce the "denominators" to given a ring or a module. That is, it introduces a new ring/module out of an existing one so that it consists of fractions :. where the denominators ''s'' range in a given subset ''S'' of ''R''. The basic example is the construction of the ring Q of rational numbers from the ring Z of rational integers. The technique has become fundamental, particularly in algebraic geometry, as it provides a natural link to sheaf theory. In fact, the term ''localization'' originates in algebraic geometry: if ''R'' is a ring of functions defined on some geometric object (algebraic variety) ''V'', and one wants to study this variety "locally" near a point ''p'', then one considers the set ''S'' of all functions which are not zero at ''p'' and localizes ''R'' with respect to ''S''. The resulting ring ''R *'' contains only information about the behavior of ''V'' near ''p''. Cf. the example given at local ring. An important related process is completion: one often localizes a ring/module, then completes. In this article, a ring is commutative with unity. == Construction == 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Localization (algebra)」の詳細全文を読む スポンサード リンク
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