V2EX modular lattice

Modular Lattice

释义 Definition

模格:在格论(lattice theory)中,一类满足“模律(modular law)”的偏序结构。直观上,它是一种介于一般格与分配格之间的结构,常用于研究代数结构(如子群格、子空间格)中的“包含关系”。

发音 Pronunciation

/mdjlr lts/(美式常见)

例句 Examples

A modular lattice is not always distributive.
模格并不一定是分配格。

In linear algebra, the lattice of subspaces of a vector space forms a modular lattice, which helps explain how sums and intersections interact.
在线性代数中,向量空间的子空间全体按包含关系构成一个模格,这有助于解释子空间的和与交如何相互作用。

词源 Etymology

Modular 来自 module(“模/模块”)的词族,进一步可追溯到拉丁语 modulus(“尺度、度量、小量”),在数学里常指满足某种“模”性质或规则。Lattice 原义是“格子、网格”(如木条交错的格栅),后来借用于数学,表示由“并(join)”与“交(meet)”两种运算组织起来的抽象结构。“Modular lattice” 作为术语,指满足特定公理(模律)的格。

相关词 Related Words

文献与作品 Literary Works

  • Garrett Birkhoff, Lattice Theory(《格论》)
  • George Grtzer, General Lattice Theory(《一般格论》)
  • B. A. Davey & H. A. Priestley, Introduction to Lattices and Order(《格与序导论》)
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