论文标题
puiseux monoid的原子性和密度
Atomicity and Density of Puiseux Monoids
论文作者
论文摘要
puiseux monoid是由$（\ mathbb {q}，+）$组成的$（Mathbb {q}，+）的子对照器。尽管相对于标准拓扑的添加操作是连续的，但通常很难描述puiseux monoid的不可减数。在本文中，我们使用拓扑密度来了解puiseux monoid及其一组不可减数，并通过$ \ mathbb {r} _ {\ ge 0} $传播。首先，我们根据$ \ mathbb {r} _ {\ ge 0} $在$ \ mathbb {r}中的密度分离puiseux monoids，并且我们以生成集合和一组inrorreducibles来表征这些类中的单体。然后，我们研究差异组的密度，根闭合和puiseux monoid的导体半群。最后，我们证明，在$ \ mathbb {r} _ {\ ge 0} $中，由严格增加的理由序列产生的每个puiseux monoid无处可去。
A Puiseux monoid is a submonoid of $(\mathbb{Q},+)$ consisting of nonnegative rational numbers. Although the operation of addition is continuous with respect to the standard topology, the set of irreducibles of a Puiseux monoid is, in general, difficult to describe. In this paper, we use topological density to understand how much a Puiseux monoid, as well as its set of irreducibles, spread through $\mathbb{R}_{\ge 0}$. First, we separate Puiseux monoids according to their density in $\mathbb{R}_{\ge 0}$, and we characterize monoids in each of these classes in terms of generating sets and sets of irreducibles. Then we study the density of the difference group, the root closure, and the conductor semigroup of a Puiseux monoid. Finally, we prove that every Puiseux monoid generated by a strictly increasing sequence of rationals is nowhere dense in $\mathbb{R}_{\ge 0}$ and has empty conductor.
