Article ID Journal Published Year Pages File Type
8896281 Journal of Algebra 2018 23 Pages PDF
Abstract
We establish necessary and sufficient conditions for a semigroup identity to hold in the monoid of n×n upper triangular tropical matrices, in terms of equivalence of certain tropical polynomials. This leads to an algorithm for checking whether such an identity holds, in time polynomial in the length of the identity and size of the alphabet. It also allows us to answer a question of Izhakian and Margolis, by showing that the identities which hold in the monoid of 2×2 upper triangular tropical matrices are exactly the same as those which hold in the bicyclic monoid. Our results extend to a broader class of “chain structured tropical matrix semigroups”; we exhibit a faithful representation of the free monogenic inverse semigroup within such a semigroup, which leads also to a representation by 3×3 upper triangular tropical matrices.
Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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