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arXiv · 1709.05277

Linear isomorphisms preserving Green's relations for matrices over semirings

Alexander Guterman·Marianne Johnson·Mark Kambites
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Abstract

In this paper we characterize those linear bijective maps on the monoid of all $n \times n$ square matrices over an anti-negative semifield which preserve and strongly preserve each of Green's equivalence relations $\mathcal{L}, \mathcal{R}, \mathcal{D}, \mathcal{J}$ and the corresponding three pre-orderings $\leq_\mathcal{L}, \leq_\mathcal{R}, \leq_\mathcal{J}$. These results apply in particular to the tropical and boolean semirings, and for these two semirings we also obtain corresponding results for the $\mathcal{H}$ relation.

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Alexander Guterman, Marianne Johnson, Mark Kambites. 2017-09-15. Linear isomorphisms preserving Green's relations for matrices over semirings. https://arxiv.org/abs/1709.05277

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