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In order-theoretic mathematics, the deviation of a poset is an ordinal number measuring the complexity of a partially ordered set. The deviation of a poset is used to define the Krull dimension of a module over a ring as the deviation of its poset of submodules. ==Definition== A poset is said to have deviation at most α (for an ordinal α) if for every descending chain of elements ''a''0 > ''a''1 >... all but a finite number of the posets of elements between ''a''''n'' and ''a''''n''+1 have deviation less than α. The deviation (if it exists) is the minimum value of α for which this is true. Not every poset has a deviation. The following conditions on a poset are equivalent: *The poset has a deviation *The opposite poset has a deviation *The poset does not contain a subset order-isomorphic to the rational numbers (with their standard numerical ordering) 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「deviation of a poset」の詳細全文を読む スポンサード リンク
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