In a ring of characteristic 2 every prime ideal is maximal ideal Let $R$ be a commutative ring with $1$ and $charR=2$.Then how can I show that every prime ideal in $R$ is a maximal ideal? I was trying to show it a boolean ring but I could not.Please Help me.Thanks

This is false.

Take $F[x]$ where $F$ is the field of two elements.

The zero ideal is prime but not maximal.