1. The problem statement, all variables and given/known data Prove that the intersection of any set of ideals of a ring is an ideal. 2. Relevant equations A nonempty subset A of a ring R is an ideal of R if: 1. a - b ε A whenever a, b ε A 2. ra and ar are in A whenever a ε A and r ε R 3. The attempt at a solution My guess is that i need to start with a collection of ideals, write a representation of the form of the intersection of those ideals, upon which i can take two generic elements and apply the ideal test above Putting this into symbols seems to be the tricky part for me. Thanks.