Abstract: In this paper it studies invertible linear operators which preserve Moore-Penrose inverse of matrices over ai-semirings, and it is completely characterized that invertible linear operators which preserve Moore-Penrose inverse of matrices over special classes of semirings, including chain semiring, distributive lattice and general Boolean algebras.

Key words: ai-semiring, linear operator, Moore-Penrose inverse

摘要： 研究了保持ai-半环上矩阵的Moore-Penrose逆的可逆线性算子，并完全刻画了保持链半环、完全分配格、n元布尔半环等特殊ai-半环上矩阵 Moore-Penrose逆的可逆线性算子。

关键词: ai-半环, 线性算子, Moore-Penrose逆