# abstract algebra – Boolean ring prime ideals

2- Prove or disprove: If $$R$$ is Boolean and $$p$$ is a prime ideal of $$R$$, then the ring homomorphism $$Rto R_p$$ is always finite.
$$bar R=R/p$$ is a boolian domain. boolian domain is a field with 2 elements. (if $$x in bar R$$, then x(1-x)=0 so x=0 or x=1 ). therefore R/p is field and $$p$$ is maximal. is this proof true?