论文标题
关于循环自由半程的代数估值的原则和弹性
On the primality and elasticity of algebraic valuations of cyclic free semirings
论文作者
论文摘要
如果每个不可矛盾的元素因素因不可减数为因素，则取消交换性单体是原子质。在某些轻度条件下，在正代数数$α$上，评估半$ \ mathbb {n} _0 [α] $的添加剂monoid $m_α$是原子。 $ \ mathbb {n} _0 [α] $的添加剂和乘法单体的原子结构都是最近几篇论文的主题。在这里，我们专注于MONOIDS $M_α$，我们研究了其欧米茄的弹性和弹性，旨在更好地了解有关其原子分解的一些基本问题。我们证明，当$α$小于1时，$M_α$的原子与可能的原子相去甚远。然后，我们对$M_α$的弹性建立了一些结果，包括当$α$是理性时，$M_α$的弹性已满（这是S. T. Chapman，F。Gotti和M. Gotti提出的）。
A cancellative commutative monoid is atomic if every non-invertible element factors into irreducibles. Under certain mild conditions on a positive algebraic number $α$, the additive monoid $M_α$ of the evaluation semiring $\mathbb{N}_0[α]$ is atomic. The atomic structure of both the additive and the multiplicative monoids of $\mathbb{N}_0[α]$ has been the subject of several recent papers. Here we focus on the monoids $M_α$, and we study its omega-primality and elasticity, aiming to better understand some fundamental questions about their atomic decompositions. We prove that when $α$ is less than 1, the atoms of $M_α$ are as far from being prime as they can possibly be. Then we establish some results about the elasticity of $M_α$, including that when $α$ is rational, the elasticity of $M_α$ is full (this was previously conjectured by S. T. Chapman, F. Gotti, and M. Gotti).
