幂半群及其算术：综述
Power monoids and their arithmetic: a survey
AI总结：
本文综述了幂半群的结构及其在非可约或非交换环境中的因式分解研究进展，探讨了其独特的算术性质。
摘要：
非空有限子集在乘法写的半群下构成一个在集论乘法下的半群。同样，包含单位元的有限子集也满足这一性质。由于其不寻常的算术特性，这些结构，通常称为幂半群，近年来引起了越来越多的关注，激发了对非可约或非交换环境中的因式分解研究的新视角。本文综述了这些发展并简要回顾了一些相关方面。
英文摘要：
The non-empty finite subsets of a multiplicatively written monoid form a monoid under setwise multiplication. The same holds for finite subsets containing the identity element. Partly due to their unusual arithmetic properties, these structures, generically known as power monoids, have attracted increasing attention in recent years, stimulating new perspectives in the study of factorizations in non-cancellative or non-commutative settings. We survey these developments and briefly review some related aspects.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
