LetRbeacommutativeringwithidentity1,where1=0.ProvethatifPisanidealinR,thenPisprimeifandonlyifR/Pisanintegraldomain.

\begin{array}{l}{\text { Let } R \text { be a commutative ring with identity } 1, \text { where } 1 eq 0 . \text { Prove that if } P \text { is an}} \\ {\text {ideal in } R, \text { then } P \text { is prime if and only if } R / P \text { is an integral domain. }}\end{array}