论文标题
总订单兼容与交换性半群中的增加
Total order compatible with addition on commutative semigroups
论文作者
论文摘要
在本文中，我们描述了所有总订单$ \ scucs $兼容与有限尺寸空间的添加性ibsemigroup $ s $相比，在有理数字上。我们提供了一个必要且充分的条件，在该条件下，配备有限的Semogroups $ S $是订单$ \ scucs $的订单良好的集合。我们还提供了一些辅助结果，以与有限维空间的添加添加的订单兼容。本文中的所有参数均基于凸的几何（不一定是封闭）集中的两个简单定理。这些定理的证明是为了方便读者的。本文的第一个版本是作为我关于牛顿理论的研究生课程的讲义。
In the paper, we describe all total orders $\succ$ compatible with addition on additive subsemigroup $S$ of finite dimensional spaces over rational numbers. We provide a necessary and sufficient condition under which a finitely generated semigroups $S$ equipped with an order $\succ$ is a well-ordered set. We also present some auxiliary results on orders compatible with addition on additive subsemigroups of finite dimensional spaces over real numbers. All arguments in this paper are based on two simple theorems in the geometry of convex (not necessarily closed) sets. Proofs of these theorems are presented for readers' convenience. A first version of this paper was written as a handout for my graduate course on the theory of Newton--Okounkov bodies.
