关于由多个几何序列生成的Puiseux幺半群的长度集合
交换代数
2020-10-26 v2
摘要
在本文中，我们研究有理多循环幺半群（即由多个几何序列生成的非负有理数加法子幺半群）的一些分解性质。特别地，我们给出了遗传原子式（即 的每个子幺半群都是原子式）的有理多循环幺半群 的完整刻画。此外，我们证明某些有理多循环幺半群的长度集合是多维算术级数的有限并，而其并集满足长度集合并集的结构定理。最后，我们将算术级数实现为某些非负有理数加法子幺半群的距离集合。
引用
@article{arxiv.2001.06158,
title = {On the sets of lengths of Puiseux monoids generated by multiple geometric sequences},
author = {Harold Polo},
journal= {arXiv preprint arXiv:2001.06158},
year = {2020}
}
备注
17 pages; in this new version we additionally prove that canonical rational multicyclic monoids satisfy the Structure Theorem for Unions of Sets of Lengths and offer a characterization of the elements of a rational multicyclic monoids that have finite set of lengths; moreover, we improve the exposition of the paper. This version will appear in Communications of the Korean Mathematical Society