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arXiv · 2609.36904

Irreducible $\mathbb Z_+$-modules over $\mathbb Z[\sqrt[m]{d_1},\sqrt[m]{d_2},\ldots, \sqrt[m]{d_r}]$

Surender Kumar·Sumandeep Kaur
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Abstract

Let $d_1,d_2,\ldots, d_r\ge 2$ be $m$-th power free positive integers. In this paper, we provide explicit representations of all irreducible $\mathbb{Z}_+$-modules over $\mathbb{Z}[\sqrt[m]{d_1},\sqrt[m]{d_2},\ldots,\sqrt[m]{d_r}]$, where $\mathbb{Z}_+$ denotes the semiring of non-negative integers.

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Surender Kumar, Sumandeep Kaur. 2026-09-29. Irreducible $\mathbb Z_+$-modules over $\mathbb Z[\sqrt[m]{d_1},\sqrt[m]{d_2},\ldots, \sqrt[m]{d_r}]$. https://arxiv.org/abs/2609.36904

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