### Abstract

Original language | English |
---|---|

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 |

### Fingerprint

### Keywords

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

### Cite this

*Journal of Algebra*,

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

**Layered tropical mathematics.** / Izhakian, Zur; Knebusch, Manfred; Rowen, Louis.

Research output: Contribution to journal › Article

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

}

TY - JOUR

T1 - Layered tropical mathematics

AU - Izhakian, Zur

AU - Knebusch, Manfred

AU - Rowen, Louis

N1 - The research of the first and third authors was supported by the Israel Science Foundation (grant No. 448/09). The research of the first author also was conducted under the auspices of the Oberwolfach Leibniz Fellows Programme (OWLF), Mathematisches Forschungsinstitut Oberwolfach, Germany. This research of the second author was supported in part by the Gelbart Institute at Bar-Ilan University, the Minerva Foundation at Tel-Aviv University, the Department of Mathematics of Bar-Ilan University, the Emmy Noether Institute at Bar-Ilan University, and the Mathematisches Forschungsinstitut Oberwolfach.

PY - 2014/10/15

Y1 - 2014/10/15

N2 - 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.

AB - 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.

KW - Tropical algebra

KW - Layered supertropical domains

KW - Polynomial semiring

KW - Resultant

KW - Sylvester matrix

KW - Discriminant

KW - Layered derivatives

U2 - 10.1016/j.jalgebra.2014.05.019

DO - 10.1016/j.jalgebra.2014.05.019

M3 - Article

VL - 416

SP - 200

EP - 273

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -