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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Distributivity (order theory) ： ウィキペディア英語版 Distributivity (order theory) In the mathematical area of order theory, there are various notions of the common concept of distributivity, applied to the formation of suprema and infima. Most of these apply to partially ordered sets that are at least lattices, but the concept can in fact reasonably be generalized to semilattices as well. ==Distributive lattices== Probably the most common type of distributivity is the one defined for lattices, where the formation of binary suprema and infima provide the total operations of join ($\backslash vee$) and meet ($\backslash wedge$). Distributivity of these two operations is then expressed by requiring that the identity : $x\; \backslash wedge\; (y\; \backslash vee\; z)\; =\; (x\; \backslash wedge\; y)\; \backslash vee\; (x\; \backslash wedge\; z)$ hold for all elements ''x'', ''y'', and ''z''. This distributivity law defines the class of distributive lattices. Note that this requirement can be rephrased by saying that binary meets preserve binary joins. The above statement is known to be equivalent to its order dual : $x\; \backslash vee\; (y\; \backslash wedge\; z)\; =\; (x\; \backslash vee\; y)\; \backslash wedge\; (x\; \backslash vee\; z)$ such that one of these properties suffices to define distributivity for lattices. Typical examples of distributive lattice are totally ordered sets, Boolean algebras, and Heyting algebras. Every finite distributive lattice is isomorphic to a lattice of sets, ordered by inclusion (Birkhoff's representation theorem). 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「Distributivity (order theory)」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.