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arXiv · 2608.30905

Irreducible $\mathbb{Z}_+$-modules over some $\mathbb{Z}_+$-rings

Yue Meng
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Abstract

Let $d_1,\ldots,d_r$ be pairwise relatively prime positive square-free integers, with $d_j\geq2$ for all $1\leq j\leq r$. Using elementary matrices and combinatorial mathematics, we give a complete classification of the irreducible $\mathbb{Z}_+$-modules over the domain $\mathbb{Z}[d^{\frac{1}{N_1}}_1,d^{\frac{1}{N_2}}_2,\dots,d^{\frac{1}{N_r}}_r]$, where $N_i \geq2$ for all $ 1\leq i \leq r$. Furthermore, we explicitly construct all of these irreducible $\mathbb{Z}_+$-modules.

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Yue Meng. 2026-08-31. Irreducible $\mathbb{Z}_+$-modules over some $\mathbb{Z}_+$-rings. https://arxiv.org/abs/2608.30905

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