The tropical Nullstellensatz for congruences

被引：16
|
作者：
Bertram, Aaron
Easton, Robert
机构：
来源：
ADVANCES IN MATHEMATICS | 2017年 / 308卷
关键词：
Tropical geometry; Congruences; Nullstellensatz; CONJECTURE; PROOF;
D O I：
10.1016/j.aim.2016.12.004
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We develop the foundations of a theory of algebraic geometry for semirings, concentrating mainly on the semiring of tropical polynomials. Replacing ideals with the more general notion of congruences, we establish a relationship between congruences on the semiring of tropical polynomials and subsets of tropical space. We ultimately establish analogues of the weak and strong forms of Hilbert's Nullstellensatz. (C) 2016 Elsevier Inc. All rights reserved.
引用
收藏
页码：36 / 82
页数：47
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