非负整数集上矩阵的积和式保持问题

Permanent preserver for matrices over the set of nonnegative integers

设R为非负整数集,用Mn(R)表示R上所有n×n矩阵构成的集合。令T是Mn(R)到其自身的线性变换,若T满足per(T(X))=per(X),X∈Mn(R),称T为Mn(R)上保持积和式的线性变换。刻画n≥2时,Mn(R)上保持积和式的加法满射,丰富半环上线性保持问题的成果。

Suppose R is the set of nonnegative integers, let Mn （R） be the set of all n × n matrices over R. A linear transformation T from Mn （R） to itself is said to be permanent preserver if per（T（X））=per （X） for every X∈Mn （R）. The surjective additive operator on Mn （R） that preserves permanent is characterized when n≥2 in this paper. The conclusion enriches the results of linear preserver problems on semiring.