If I and J are ideals of R, prove that their intersection is also an ideal of R
Hence show that the intersection of an arbitrary nonempty is again an ideal (do not assume that the collection is countable)
Would appreciate help with this exercise ... my main problem is with generalising to an uncountable collection
Peter
I and J ideals of R is an ideal of R
Proof
.... (1)
for all
..... (1)
(1) , (2) is ideal of R
Then since is an ideal, use the above proof on K and to show is an ideal and so on for countably many ideals.