{"paper":{"title":"Linear isomorphisms preserving Green's relations for matrices over semirings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Alexander Guterman, Marianne Johnson, Mark Kambites","submitted_at":"2017-09-15T15:42:43Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05277","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}