半群部分内自同构的逆单子
群论
2026-05-04 v1
摘要
我们引入了半群部分内自同构的逆单子——这一工具可将每个半群关联到一个逆单子。当半群为群时，这一逆单子等价于加上零元后的内自同构群。随后，我们描述了该结构在完全简单半群、全变换半群以及有限G-集的内同构单子中的情况（当G为有限阿贝尔群时）。本文以若干开放问题收尾。
引用
@article{arxiv.2605.00041,
title = {The Inverse Monoid of Partial Inner Automorphisms of a Semigroup},
author = {João Araújo and Wolfram Bentz and Michael Kinyon and Janusz Konieczny António Malheiro and Valentin Mercier},
journal= {arXiv preprint arXiv:2605.00041},
year = {2026}
}
备注
This paper was originally section 5 of arXiv:2301.04252 . We spun it off into its own paper at the suggestion of the referee. If the arXiv system flags it for substantial text overlap, that's why. arXiv admin note: substantial text overlap with arXiv:2301.04252