格矩阵半群的Euler-Fermat公式(英文)

On the Euler-Fermat Formula for the Semigroup of Lattice Matrices

给出并证明格矩阵半群的Euler-Fermat公式:A(n-1)2+1=A(n-1)2+1+[n],A∈Mn(L)其中L是任意的分配格,Mn(L)是L上所有n阶矩阵构成的半群。这是布尔矩阵半群的Euler-Fermat公式的一种推广。

This paper formalizes and proves the Euler-Fermat formula for the semigroup of lattice matrices ： A^（n-1）^2＋1=A^（n-1）^2＋1＋[a],A∈Mn（L）where L is an arbitrary distributive lattice and M. （L） is the semigroup of all n X n matrices over L. It is a generalization of the Euler-Fermat formula for the semigroup of Boolean matrices.