论文标题
关于指数puiseux monoids和semirings的原子结构
On the atomic structure of exponential Puiseux monoids and semirings
论文作者
论文摘要
puiseux monoid是理性数字的非负锥的加性下monoid。我们说Puiseux monoid $ m $是指数，只要存在一个正理性$ r $和一个由非负整数组成的套装$ s $，其中包含$ 0 $，这样$ m $是由set $ \ \ {r^s \ s \ mid s \ in s \} $生成的。如果$ m $多重关闭，那么我们说$ m $是指数的puiseux semiring。在这里，我们研究了指数puiseux himoids和semirings的原子特性。首先，我们表征了原子指数puiseux monoids，并证明有限的分解属性，有界的分解属性和ACCP在这种情况下重合。然后，我们继续提供必要的条件和足够的条件，使指数puiseux monoid满足ACCP。我们通过描述指数的puiseux himoids是半肌的结论。
A Puiseux monoid is an additive submonoid of the nonnegative cone of the rational numbers. We say that a Puiseux monoid $M$ is exponential provided that there exist a positive rational $r$ and a set $S$ consisting of nonnegative integers, which contains $0$, such that $M$ is generated by the set $\{r^s \mid s \in S\}$. If $M$ is multiplicatively closed then we say that $M$ is an exponential Puiseux semiring. Here we study the atomic properties of exponential Puiseux monoids and semirings. First, we characterize atomic exponential Puiseux monoids, and we prove that the finite factorization property, the bounded factorization property, and the ACCP coincide in this context. Then we proceed to offer a necessary condition and a sufficient condition for an exponential Puiseux monoid to satisfy the ACCP. We conclude by describing the exponential Puiseux monoids that are semirings.
