Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Kopp, Gene S.
Institution: Louisiana State University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7221199113