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In mathematics, a ringed space can be equivalently thought of either :(a) a space together with a collection of commutative rings, the elements of which are "functions" on each open set of the space, or :(b) a family of (commutative) rings parametrized by open subsets of a topological space, together with ring homomorphisms coming from the relationships between open sets; in short, the sheaf of rings. Ringed spaces appear in analysis as well as complex algebraic geometry and scheme theory of algebraic geometry. The point of view (b) is more amenable to generalization; one simply needs to cook up a different way of parametrizing rings (cf. ringed topos.) Note: Many expositions tend to restrict the rings to be commutative rings, including Hartshorne and Wikipedia, in the definition of a ringed space. "Éléments de géométrie algébrique", on the other hand, does not impose the commutativity assumption, although the book only considers the commutative case. (EGA, Ch 0, 4.1.1.) ==Definition== Formally, a ringed space (''X'', ''O''''X'') is a topological space ''X'' together with a sheaf of rings ''O''''X'' on ''X''. The sheaf ''O''''X'' is called the structure sheaf of ''X''. A locally ringed space is a ringed space (''X'', ''O''''X'') such that all stalks of ''O''''X'' are local rings (i.e. they have unique maximal ideals). Note that it is ''not'' required that ''O''''X''(''U'') be a local ring for every open set ''U.'' In fact, that is almost never going to be the case. 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「Ringed space」の詳細全文を読む スポンサード リンク
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