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Semigroup identities of tropical matrix semigroups of maximal rank

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Abstract

We show that any semigroup of n-by-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-by-n triangular tropical matrices.

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Acknowledgments

The author would like to thank the referee for his comments and helpful suggestions.

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  1. Institute of Mathematics, University of Aberdeen, Aberdeen, AB24 3UE, UK

    Zur Izhakian

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  1. Zur Izhakian
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Correspondence to Zur Izhakian.

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Communicated by Jean-Eric Pin.

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Izhakian, Z. Semigroup identities of tropical matrix semigroups of maximal rank. Semigroup Forum 92, 712–732 (2016). https://doi.org/10.1007/s00233-015-9765-6

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  • DOI: https://doi.org/10.1007/s00233-015-9765-6

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