布尔代数上强保持交换矩阵对的线性算子

Linear operators that strongly preserve commuting pairs of matrices over Boolean algebras

设 B是一个具有最大元 1和最小元 0的布尔代数 ,Mn( B)是 B上n阶矩阵半环 ,L是Mn( B)上的一个线性算子 ,如果 A ,B∈Mn( B) ,均有AB =BA当且仅当L(A)L(B) =L(B)L(A) ,则称L强保持Mn( B)中的交换矩阵对 .本文刻画了布尔代数上强保持交换矩阵对的线性算子 .

Let be a Boolean algebra and M n() be the semiring of all matrices of order n over . For a linear operator L on M n(), we say that L strongly preserve commuting pairs of matrices if for any A and B in M n(), AB=BA if and only if L(A)L(B) =L(B)L(A). In this paper, the linear operators that strongly preserve commuting pairs of matrices over are characterized.