Idempotent factorization on some matrices over quadratic integer rings

Peeraphat Gatephan, Kijti Rodtes

In 2020, Cossu and Zanardo raised a conjecture on the idempotent factorization on singular matrices in the form $\begin{pmatrix} p&z\\ \bar{z}&\sfrac{\lVert z\rVert}{p} \end{pmatri…