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cubixguy77
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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.