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arXiv · 2610.11353

Ray class monoids for orders of number fields

Gene S. Kopp
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Abstract

We define and study six ray class monoids associated to a level datum $(\mathcal{O}; \mathfrak{m}, Σ)$, where $\mathcal{O}$ is an order in a number field $K$, $\mathfrak{m}$ is an $\mathcal{O}$-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.

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Gene S. Kopp. 2026-10-08. Ray class monoids for orders of number fields. https://arxiv.org/abs/2610.11353

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