Semigroup identities of tropical matrix semigroups of maximal rank. (English) Zbl 1377.15016
Semigroup Forum 92, No. 3, 712-732 (2016); erratum ibid. 97, No. 3, 571 (2018).
It is shown that any semigroup of \(n\times n\) tropical matrices whose elements all have rank \(n\) (i.e. a nonsingular semigroup) satisfies a class of nontrivial semigroup identities. These identities generalize the identities satisfied by the monoid of all \(n\times n\) triangular tropical matrices.
Reviewer: Andreas Arvanitoyeorgos (Patras)
Keywords:
tropical (max-plus) matrix algebra; semigroup identities; semigroup varieties; semigroup representations; nonsingular matrices; rank-maximal semigroupsReferences:
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