  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
$\mathbb{Z}/n\mathbb{Z} \times \mathbb{Z}/m\mathbb{Z}$.
