A finite subring $R$ of a field $V$ contains $1$ (so $1$ is an element of $R$).
The question is: True or False: The ring $R$ must be a field.
I thought that if $R$ was a field it had to be a finite field in this case (because $R$ is a finite ring). And to be able to be a finite field, it should have $ |R| = p^n $ With $p$ a prime and $n$ a natural number, but this doesn't have to be the case.
I could be wrong or what I'm saying could be insufficient to prove this right or wrong.
Please help ^^