言语不易：多循环幺半群的强仿射表示
Words don't come easy: strong affine representations of the polycyclic monoids
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中文总结 AI 辅助
研究多循环幺半群$\mathcal{P}_n$的一维强仿射表示，在剩余系为等差数列时，通过引入闭包算子刻画，涵盖了$\mathcal{P}_2$的相关表示。
中文摘要 AI 辅助
多循环幺半群$\mathcal{P}_n$的每个一维强仿射表示由模$n$的完全剩余系诱导。当剩余系为等差数列时，我们完全刻画了这些表示。通过在$\{0,1,\dots,n - 1\}$上的本原词集引入闭包算子来实现，并描述了闭集格。此刻画涵盖了$\mathcal{P}_2$的所有一维强仿射表示。
英文摘要
Each one-dimensional strong affine representation of the polycyclic monoid $\mathcal{P}_n$ is induced by a complete system of residues modulo $n$. We completely characterize these representations in the case when the system of residues is an arithmetic sequence. We accomplish this by introducing a closure operator on the set of primitive words over $\{0,1,\dots,n-1\}$, and we also describe the lattice of closed sets. This characterization covers all one-dimensional strong affine representations of $\mathcal{P}_2$.
