Supertropical polynomials and resultants

Zur Izhakian; Louis Rowen

doi:10.1016/j.jalgebra.2010.05.019

Supertropical polynomials and resultants

Zur Izhakian, Louis Rowen

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

This paper, a continuation of Izhakian and Rowen (in press) [5], involves a closer study of polynomials over supertropical semirings and their version of tropical geometry. We introduce the concept of relatively prime polynomials (in one indeterminate) and resultants, with the aid of some topology. Polynomials in one indeterminant are seen to be relatively prime iff they do not have a common tangible root, iff their resultant is tangible. Applying various morphisms of supertropical varieties leads to a supertropical version of Bézout's theorem.

Original language	English
Pages (from-to)	1860-1886
Number of pages	27
Journal	Journal of Algebra
Volume	324
Issue number	8
DOIs	https://doi.org/10.1016/j.jalgebra.2010.05.019
State	Published - Oct 2010

Bibliographical note

Funding Information:
✩ This work has been supported in part by the Israel Science Foundation, grant 1178/06, and by grant No. 448/09.

Funding

✩ This work has been supported in part by the Israel Science Foundation, grant 1178/06, and by grant No. 448/09.

Funders	Funder number
Israel Science Foundation	448/09, 1178/06

Keywords

Bézout's theorem
Matrix algebra
Relatively prime
Resultant
Supertropical algebra
Supertropical polynomials

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10.1016/j.jalgebra.2010.05.019

Cite this

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author = "Zur Izhakian and Louis Rowen",

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AU - Rowen, Louis

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AB - This paper, a continuation of Izhakian and Rowen (in press) [5], involves a closer study of polynomials over supertropical semirings and their version of tropical geometry. We introduce the concept of relatively prime polynomials (in one indeterminate) and resultants, with the aid of some topology. Polynomials in one indeterminant are seen to be relatively prime iff they do not have a common tangible root, iff their resultant is tangible. Applying various morphisms of supertropical varieties leads to a supertropical version of Bézout's theorem.

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KW - Matrix algebra

KW - Relatively prime

KW - Resultant

KW - Supertropical algebra

KW - Supertropical polynomials

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SP - 1860

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JO - Journal of Algebra

JF - Journal of Algebra

IS - 8

ER -

Supertropical polynomials and resultants

Abstract

Bibliographical note

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Keywords

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