Resultants over Commutative Idempotent Semirings
Rings and Algebras
2015-05-26 v1
Abstract
The resultant plays a crucial role in (computational) algebra and algebraic geometry. One of the most important and well known properties of the resultant is that it is equal to the determinant of the Sylvester matrix. In 2008, Odagiri proved that a similar property holds over the tropical semiring if one replaces subtraction with addition. The tropical semiring belongs to a large family of algebraic structures called commutative idempotent semiring. In this paper, we prove that the same property (with subtraction replaced with addition) holds over an \emph{arbitrary\/} commutative idempotent semiring.
Cite
@article{arxiv.1505.06470,
title = {Resultants over Commutative Idempotent Semirings},
author = {Hoon Hong and Yonggu Kim and Georgy Scholten and J. Rafael Sendra},
journal= {arXiv preprint arXiv:1505.06470},
year = {2015}
}