论文标题
超级线引起的半段系统
Semiring systems arising from hyperrings
论文作者
论文摘要
Hyperfields和系统是两个代数框架，这些框架已开发出来，为经典和热带结构提供统一的方法。所有Hyperfields和更普遍的超级线都可以由系统表示。相反，我们表明以这种方式产生的系统称为{\ it Hypersystems}，其特征是某些消除公理。系统保留在标准代数结构下；例如，超级系统的矩阵和多项式是系统，而不是超系统。我们通过讨论系统和高场的几个示例以及系统上的构造来说明这些结果。
Hyperfields and systems are two algebraic frameworks which have been developed to provide a unified approach to classical and tropical structures. All hyperfields, and more generally hyperrings, can be represented by systems. Conversely, we show that the systems arising in this way, called {\it hypersystems}, are characterized by certain elimination axioms. Systems are preserved under standard algebraic constructions; for instance matrices and polynomials over hypersystems are systems, but not hypersystems. We illustrate these results by discussing several examples of systems and hyperfields, and constructions like matroids over systems.
