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Is the max-plus algebra an example of tropical mathematics or is it an independent structure? How can we turn a max-plus algebra into tropical geometry or viceversa-if possible?

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  • $\begingroup$ It would be helpful if we know how much tropical geometry you know. What would you consider "being turned into tropical geometry?" $\endgroup$ – Cheerful Parsnip Apr 29 '13 at 18:08
  • $\begingroup$ I have read the "classical" reviews in the arxiv for newbies. I think I understand now that min-plus/max-plus algebras are both tropical, but I wonder if they are "isomorphic" somehow... $\endgroup$ – riemannium May 1 '13 at 16:12
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    $\begingroup$ Just take the functor $F$ sending the max operator to the min operator and each element to it's negative. Should be able to show easily then that this gives an algebra isomorphism. $\endgroup$ – Andrew Whelan Dec 5 '18 at 17:46
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A max-plus algebra is a tropical algebra. See: http://arxiv.org/PS_cache/math/pdf/0507/0507014v1.pdf

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