PreprintCC0arXiv
Irreducible ℤ+-modules over some ℤ+-rings
Abstract
Let d1,…,dr be pairwise relatively prime positive square-free integers, with dj≥2 for all 1≤ j≤ r. Using elementary matrices and combinatorial mathematics, we give a complete classification of the irreducible ℤ+-modules over the domain ℤ[d1/N11,d1/N22,…,d1/Nrr], where Ni ≥2 for all $ 1\leq i \leq r$. Furthermore, we explicitly construct all of these irreducible ℤ+-modules.
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BibTeX
@misc{meng2026irreducible,
title = {{Irreducible $\mathbbZ_+$-modules over some $\mathbbZ_+$-rings}},
author = {Yue Meng},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30905},
eprint = {2608.30905},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30905},
note = {CC0},
}
RIS
TY - UNPB
TI - Irreducible ℤ_+-modules over some ℤ_+-rings
AU - Yue Meng
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30905
UR - https://arxiv.org/abs/2608.30905
AB - Let d_1,…,d_r be pairwise relatively prime positive square-free integers, with d_j≥2 for all 1≤ j≤ r. Using elementary matrices and combinatorial mathematics, we give a complete classification of the irreducible ℤ_+-modules over the domain ℤ[d^1/N_1_1,d^1/N_2_2,…,d^1/N_r_r], where N_i ≥2 for all $ 1\leq i \leq r$. Furthermore, we explicitly construct all of these irreducible ℤ_+-modules.
ER -