A counting formula in modular lattices and it's applications in algebra
Kezheng Zuo · Journal of Hubei Normal University · 2009
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.