### Abstract

Generalizing supertropical algebras, we present a “layered” structure, “sorted” by a semiring which permits varying ghost layers, and indicate how it is more amenable than the “standard” supertropical construction in factorizations of polynomials, description of varieties, and for mathematical analysis and calculus, in particular with respect to multiple roots of polynomials. This gives rise to a significantly better understanding of the tropical resultant and discriminant. Explicit examples and comparisons are given for various sorting semirings such as the natural numbers and the positive rational numbers, and we see how this theory relates to some recent developments in the tropical literature.

Original language | English |
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Pages (from-to) | 200-273 |

Number of pages | 74 |

Journal | Journal of Algebra |

Volume | 416 |

Early online date | 11 Jul 2014 |

DOIs | |

Publication status | Published - 15 Oct 2014 |

### Keywords

- Tropical algebra
- Layered supertropical domains
- Polynomial semiring
- Resultant
- Sylvester matrix
- Discriminant
- Layered derivatives

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## Cite this

Izhakian, Z., Knebusch, M., & Rowen, L. (2014). Layered tropical mathematics.

*Journal of Algebra*,*416*, 200-273. https://doi.org/10.1016/j.jalgebra.2014.05.019