Remark 2

Remark 1 shows that if $A$ is a ring of characteristic 0 (resp. $p \neq 0$), the same holds of any ring $A'$ containing $A$ as subring, or of any quotient of $A$ by a two-sided ideal $a \neq A$. In particular, if $K$ is a field, every subfield of $K$ and every extension field of $K$ have the same characteristic as $K$.