Z/(m)上N级全矩阵环零因子个数的估计

The Estimation of the Number of Zero Divisors in the Matrix Ring Over Z / (m)

在研究了Z/(p^m)上n级全矩阵环零因子个数的最佳估计基础上,本文进一步得到更一般的有限剩余类环Z/(m)上n级全矩阵环零因子数目的最佳估计,其中m是自然数,m>2.

Let R(m)=Z/ (m) be the finite residue class ring, E_n(R(m)) be the ring of N×n matrices over R(m); let O[E_n(R(m))] be the number of elements in E_n(R(m)) and S[E_n(R(m))] be the number of zero divisors in E_n(R(m)).It is proved that O[E_n (R(m))] is less than S[E_n(R(m))]^(1+(1/(n(n-1))).