| 翻訳と辞書 |
| algebraic matroid ： ウィキペディア英語版 |
algebraic matroid
In mathematics, an algebraic matroid is a matroid, a combinatorial structure, which expresses an abstraction of the relation of algebraic independence.
==Definition==
Given a field extension ''L''/''K'', Zorn's lemma can be used to show that there always exists a maximal algebraically independent subset of ''L'' over ''K''. Further, all the maximal algebraically independent subsets have the same cardinality, known as the transcendence degree of the extension.
For every set ''S'' of elements of ''L'', the algebraically independent subsets of ''S'' satisfy the axioms that define the independent sets of a matroid. In this matroid, the rank of a set of elements is its transcendence degree, and the flat generated by a set ''T'' of elements is the intersection of ''L'' with the field ''K''().〔Oxley (1992) p.216〕 A matroid that can be generated in this way is called ''algebraic'' or ''algebraically representable''.〔Oxley (1992) p.218〕 No good characterization of algebraic matroids is known,〔Oxley (1992) p.215〕 but certain matroids are known to be non-algebraic; the smallest is the Vámos matroid.〔.〕〔
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「algebraic matroid」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.
|
|