= Solution
An <ideal> $I$ of a commutative ring is an additive subgroup such that $rx\in I$ for every $r\in R$ and $x\in I$. A <prime ideal> is a proper <ideal> $A\neq R$ such that $xy\in A$ implies $x\in A$ or $y\in A$.
If $(x+A)(y+A)=0+A$ in the <quotient ring>, then $xy\in A$. Primality implies $x+A=0+A$ or $y+A=0+A$. Therefore there are no two nonzero cosets whose product is zero:
$$
\boxed{R/A\text{ has no nonzero zero-divisors}.}
$$
Properness also ensures its identity coset is not zero, so this quotient is an <integral domain>.
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