cubixguy77
Nov23-08, 08:24 PM
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.
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.