关于指数Pui-x半环的加法结构的因子分解不变量
On the factorization invariants of the additive structure of exponential Puiseux semirings
摘要：
指数Puixix半环是由正有理数的几乎所有非负幂生成的$\qq_{\geq 0}$的加法子幺半群，是有理循环半环的自然推广.在本文中，我们研究了指数Pui-x半环的一些因子分解不变量，并简要地探讨了这些性质与半群理论不变量之间的联系。具体地说，我们证明了原子指数Pui-x半环的长度集几乎是具有公共界的等差数列，而长度集的并集是等差数列。此外，我们提供了精确的公式来计算这些幺半群的悬链线度，并表明，他们的距离集的最小值和最大值总是达到贝蒂元素。最后，我们提供了各种表征的原子指数Puixix半环与有限的欧米茄功能，特别是，我们完全描述他们的介绍。
英文摘要：
Exponential Puiseux semirings are additive submonoids of $\qq_{\geq 0}$ generated by almost all of the nonnegative powers of a positive rational number, and they are natural generalizations of rational cyclic semirings. In this paper, we investigate some of the factorization invariants of exponential Puiseux semirings and briefly explore the connections of these properties with semigroup-theoretical invariants. Specifically, we prove that sets of lengths of atomic exponential Puiseux semirings are almost arithmetic progressions with a common bound, while unions of sets of lengths are arithmetic progressions. Additionally, we provide exact formulas to compute the catenary degrees of these monoids and show that minima and maxima of their sets of distances are always attained at Betti elements. We conclude by providing various characterizations of the atomic exponential Puiseux semirings with finite omega functions; in particular, we completely describe them in terms of their presentations.
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