Sentence:  In trying to understand the ideal theory of a commutative ring, one quickly sees that it is important to first understand the <WSD>prime ideals</WSD>. We recall that a proper ideal P in a commutative ring R is prime if, whenever we have two elements a and b of R such that ab\in P, it follows that a\in P or b\in P; equivalently, P is a <WSD>prime ideal</WSD> if and only if the factor ring R/P is a domain. 
Meaning of the word marked with <WSD> tags:  Any (two-sided) ideal I such that for arbitrary ideals P and Q, PQ\subseteq I\implies P\subseteq I or Q\subseteq I.