论文标题
在按比例的模块化数值半群上，算术进行了
On proportionally modular numerical semigroups that are generated by arithmetic progressions
论文作者
论文摘要
数值半群是$ {\ mathbb z} _ {\ ge 0} $的submonoid，其补充$ {\ mathbb z} _ {\ ge 0} $是有限的。对于任何集体整数$ a，b，c $，由不等式$ ax \ ax \ bmod {b} \ le cx $形成的数值半群$ s（a，b，c）$ the形成。对于任何间隔$ [α，β] $，$ s \ big（[[α，β] \ big）$是$ {\ Mathbb z} _ {\ ge 0} $的subonoid，该$由$ {\ Mathb Q} _ {\ ge ge 0} $ n $ n $ { z} _ {\ ge 0} $。 对于给定算术进程产生的数值半群$ s $，我们表征$ a，b，c $和$α，β$，使得$ s（a，b，c）$和$ s \ big（[α，β] \ big）$ s $相等。
A numerical semigroup is a submonoid of ${\mathbb Z}_{\ge 0}$ whose complement in ${\mathbb Z}_{\ge 0}$ is finite. For any set of positive integers $a,b,c$, the numerical semigroup $S(a,b,c)$ formed by the set of solutions of the inequality $ax \bmod{b} \le cx$ is said to be proportionally modular. For any interval $[α,β]$, $S\big([α,β]\big)$ is the submonoid of ${\mathbb Z}_{\ge 0}$ obtained by intersecting the submonoid of ${\mathbb Q}_{\ge 0}$ generated by $[α,β]$ with ${\mathbb Z}_{\ge 0}$. For the numerical semigroup $S$ generated by a given arithmetic progression, we characterize $a,b,c$ and $α,β$ such that both $S(a,b,c)$ and $S\big([α,β]\big)$ equal $S$.
