一类半环上的行列式保持问题研究

Research on determinant preserver over a class of semiring

设R为非负交换整半环,用Mn(R)表示R上所有n×n矩阵构成的矩阵半环。在非负交换整半环上的矩阵半环Mn(R)上分别刻画保持正行列式、负行列式、积和式的线性算子形式,丰富半环上线性保持问题的成果。

Suppose is nonnegative commutative semiring without zero divisors, let be the matrix semiring of all matrices over. The forms of the linear transformation on which preserve positive determinant,negative determinant, permanent are characterized in this paper. The conclusion enriches the results of linear preserver problems on semiring.