1. The problem statement, all variables and given/known data From contemporary abstract algebra : http://gyazo.com/08def13b62b0512a23505811bcc1e37e 2. Relevant equations "A subring A of a ring R is called a (two-sided) ideal of R if for every r in R and every a in A both ra and ar are in A." So I know that since A and B are ideals of a ring R, [itex]ar, ra \in A[/itex] and [itex]br, rb \in B[/itex] for all [itex]a \in A, \space b \in B, \space r \in R[/itex] 3. The attempt at a solution So my guess is to argue the double inclusion for this. Case : [itex]A \cap B \subseteq AB[/itex] Suppose [itex]k \in A \cap B[/itex], then [itex]k \in A[/itex] and [itex]k \in B[/itex]. We want to show [itex]k \in AB[/itex] I'm having trouble seeing how the given facts are supposed to steer the argument from here. Help would be much appreciated.