论文标题
在数值单体的幂型幂的代数性质上
On algebraic properties of power monoids of numerical monoids
论文作者
论文摘要
令$ s \ subset \ mathbb {n} _0 $为数字单体，让$ \ Mathcal p _ {\ Mathrm {fin}}（s）$，ersp $ \ mathcal p _ {\ mathrm {\ mathrm {fin}，0}，0}（s） $ s $的限制功率单体是$ s $，resp.s $的所有有限的非发空子集的集合。包含0的$ s $的所有有限的非发行子集的集合，并将添加作为操作。电源算术在最近的文献中受到了一些关注。我们通过研究功率单体（例如它们的原始频谱）的代数特性来补充这些研究。此外，我们证明，$ \ Mathcal P _ {\ Mathrm {fin}，0}（s）$的几乎所有元素都是不可约的（即它们不是合适的总和），从而定量改善了沿途的shitov的结果。
Let $S \subset \mathbb{N}_0$ be a numerical monoid and let $\mathcal P_{\mathrm{fin}} (S)$, resp $\mathcal P_{\mathrm{fin},0}(S)$, denote the power monoid, resp. the restricted power monoid, of $S$, that is the set of all finite nonempty subsets of $S$, resp. the set of all finite nonempty subsets of $S$ containing 0, with set addition as operation. The arithmetic of power monoids received some attention in recent literature. We complement these investigations by studying algebraic properties of power monoids, such as their prime spectrum. Moreover, we prove that almost all elements of $\mathcal P_{\mathrm{fin},0} (S)$ are irreducible (i.e., they are not proper sumsets), quantitatively improving a result of Shitov along the way.
