$\lambda$-quiddit\'es sur des produits directs d'anneaux

TL;DR

This paper extends the study of $\lambda$-quiddity over rings, focusing on direct products of rings, including those with characteristic zero and specific modular rings, to understand their algebraic properties.

Contribution

It investigates $\lambda$-quiddity over direct product rings, particularly those with characteristic zero and certain modular rings, advancing the algebraic understanding of these structures.

Findings

Characterization of $\lambda$-quiddity in direct product rings.

Analysis of $\lambda$-quiddity in rings with characteristic zero.

Study of $\lambda$-quiddity in rings of the form $\mathbb{Z}/n\mathbb{Z} imes \mathbb{Z}/m\mathbb{Z}$.

Abstract

The aim of this article is to continue the study of the notion of $\lambda$-quiddity over a ring, which appeared during the study of Coxeter's friezes. For this, we will focus here on situations where the ring used can be seen as a direct product of unitary commutative rings. In particular, we will consider the cases of direct products of rings containing at least two rings of characteristic 0 and we will also consider some products of the type $\mathbb{Z}/n\mathbb{Z} \times \mathbb{Z}/m\mathbb{Z}$.