Proving Intersection of Ideals is an Ideal

[cubixguy77]

Homework Statement

Prove that the intersection of any set of ideals of a ring is an ideal.

Homework 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

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.

 

[morphism]

You don't need a representation of the form of the intersection. Just apply the definition directly. For example, to apply 1, take a & b in the intersection. What can you say about a-b?