Abstract:We determine minimal generating sets for matrix monoids over semirings and semifields. In particular, we produce minimal generating sets for the monoids of upper triangular and unitriangular matrices over a commutative semiring. We construct minimal and irredundant generating sets for the monoids of 2 × 2 and 3 × 3 matrices over the tropical integers, showing that M3(Zmax) is not finitely generated.
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