Source: cirosantilli/classification-of-finite-rings
= Classification of finite rings
{tag=Classification (mathematics)}
$M_n(\F_q)$ accounts for them all, which we know how to do due to the <classification of finite fields>.
So we see that the classification is quite simple, much like the <classification of finite fields>, and in strict opposition to the <classification of finite simple groups> (not to mention the 2023 lack of classification for non simple finite groups!)