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词汇 Maximal element
分类 英语词汇 英语翻译词典
释义

Maximal element

英语例句库

Using the notion of coefficient matrix and maximal element.We prove that the Lie algebra is semi-simple and it has no abelian two dimensional subalgebra.

利用系数矩阵和极大项，证明了这类李代数是半单李代数且没有二维交换子代数。

中文百科

极大元

设(A, \leq)是偏序集，B \subseteq A，y \in B，若对于所有的x \in B，y \leq x ~\implies~x = y，则称y为B的极大元。

请注意极大元和最大元的区别。最大元是B中最大的元素，它与B中其它元素都可比；而极大元不一定与B中其它元素都可比，只要没有比它大的元素，它就是极大元。对于有穷集合B，极大元一定存在，但最大元不一定存在。最大元如果存在一定是唯一的，但极大元可能有多个。

英语百科

Maximal element 极大元

A fence consists of minimal and maximal elements only (Example 3).
Power set of x,y,z, partially ordered by ⊂. Its greatest element, x,y,z, is its only maximal element.

In mathematics, especially in order theory, a maximal element of a subset S of some partially ordered set (poset) is an element of S that is not smaller than any other element in S. A minimal element of a subset S of some partially ordered set is defined dually as an element of S that is not greater than any other element in S.
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