Maximal Ideals

I have a theorem which says:

If the ideal $I$ is maximal, then $R/I$ is a field.

Is the converse true, can you say that if $R/I$ is a field, then $I$ is maximal??

Thanks!

You need R to be commutative as well don't you?

The converse is true. Perhaps you have a theorem that says:

If R is commutative with an identity element then R is a field if and only if the only ideals of R are {0} and R

Also, you need the third isomorphism theorem:

If R is a ring and I and ideal of R, there is a one to one correspondence between ideals J so that $I \subseteq J \subseteq R$ and ideals of R/I.

Then R/I is a field if and only if the ideals of R/I are R/I and {0} if and only if there are no ideals strictly between I and R (which is what it means for I to be maximal).