摘要
证明了模格中的维数计算公式,同时给出了分配格中的维数计算公式。由此证明了代数学其他领域中的几个重要的计数公式:组合学中的容斥原理;数论中多个整数的最大公因数与最小公倍数的计算公式;线性代数中线性子空间的和与交的维数计算公式;群论中有限正规子群的积与交的计算公式。从而将这些计数问题统一起来。
In this paper the calculation formulae of dimension in modular lattices and distributive lattices are given. By them we get some important counting formulae in other algebra fields ： including - excluding principle in Combinatorics; calculation formulae on the grestest common divisor and the least common multiple of several integers in Number Theory; calculation dimension formulae on the sum and the meet of subspaces in Linear Algebra; the calculation formulae of dimension on the product and the meet of finite normal subgroups in Group Theory. Then these counting problems are unified.
出处
《湖北师范学院学报（自然科学版）》
2009年第1期15-18,共4页
Journal of Hubei Normal University(Natural Science)
基金
湖北师范学院教研项目(200719
200821)
关键词
维数公式
模格
容斥原理
最大公因数
最小公倍数
正规子群
dimension formulae
modular lattices
including - excluding principle
the grestest common divisor
the least common multiple
the least common multiple
normal subgroups
