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Ray class monoids for orders of number fields
Abstract
We define and study six ray class monoids associated to a level datum (𝒪; m, Σ), where 𝒪 is an order in a number field K, m is an 𝒪-ideal, and Σ is a set of real places of K. The monoids extend the ray class group (and the ring class group) by including non-invertible classes consisting of non-invertible ideals and ideals not coprime to the modulus. We prove fundamental results on the structure of these ray class monoids.
Related
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BibTeX
@misc{kopp2026class,
title = {{Ray class monoids for orders of number fields}},
author = {Gene S. Kopp},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11353},
eprint = {2610.11353},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11353},
}
RIS
TY - UNPB
TI - Ray class monoids for orders of number fields
AU - Gene S. Kopp
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11353
UR - https://arxiv.org/abs/2610.11353
AB - We define and study six ray class monoids associated to a level datum (𝒪; m, Σ), where 𝒪 is an order in a number field K, m is an 𝒪-ideal, and Σ is a set of real places of K. The monoids extend the ray class group (and the ring class group) by including non-invertible classes consisting of non-invertible ideals and ideals not coprime to the modulus. We prove fundamental results on the structure of these ray class monoids.
ER -