论文标题
在由多个几何序列产生的puiseux单体长度的集合上
On the sets of lengths of Puiseux monoids generated by multiple geometric sequences
论文作者
论文摘要
在本文中，我们研究了有理多环体单体的某些分解方面，即由多个几何序列产生的非负合理数的加性下monoids。特别是，我们提供了遗传原子上有理多环状$ m $的完整描述（即，$ m $的每个亚monoid is is otomic is atomic is amonoid is otomic）。此外，我们表明，某些有理多环体单体的长度集是多维算术渐进的有限工会，而其工会则满足了一组长度的结构定理。最后，我们意识到算术进程是非负合理数字的某些添加剂亚monoi的距离集。
In this paper, we study some of the factorization aspects of rational multicyclic monoids, that is, additive submonoids of the nonnegative rational numbers generated by multiple geometric sequences. In particular, we provide a complete description of the rational multicyclic monoids $M$ that are hereditarily atomic (i.e., every submonoid of $M$ is atomic). Additionally, we show that the sets of lengths of certain rational multicyclic monoids are finite unions of multidimensional arithmetic progressions, while their unions satisfy the Structure Theorem for Unions of Sets of Lengths. Finally, we realize arithmetic progressions as the sets of distances of some additive submonoids of the nonnegative rational numbers.
