Journal of the
Korean Mathematical Society JKMS

We consider linear operators on square matrices over antinegative semirings. Let $\E_k$ denote the set of all primitive matrices of exponent $k$. We characterize those linear operators which preserve the set $\E_1$ and the set $\E_2$, and those that preserve the set $\E_{n^2-2n+2}$ and the set $\E_{n^2-2n+1}$. We also characterize those linear operators that strongly preserve $\E_2$, $\E_{n^2-2n+2}$ or $\E_{n^2-2n+1}$.

Keywords: Linear operator, primitive matrix, line matrix, double star matrix

MSC numbers: Primary 15A04, 15A86, 15B34