Concept:
Advanced ceramics are classified into oxide ceramics and non-oxide ceramics.
Step 1: Alumina is:
\[
Al_2O_3
\]
So it is an oxide ceramic.
Step 2: Zirconia is:
\[
ZrO_2
\]
So it is also an oxide ceramic.
Step 3: Magnesia is:
\[
MgO
\]
So it is also an oxide ceramic.
Step 4: Silicon nitride is:
\[
Si_3N_4
\]
It does not contain oxygen as the main anion.
Therefore, silicon nitride is a non-oxide ceramic:
\[
\boxed{\text{Silicon nitride}}
\]