Henrique observed that for Proposition 1.20 to be true for the ideal
[latex]I=R[/latex], which has no prime ideals containing it, one needs to
interpret the intersection of no prime ideals at all to be the unit ideal.
That is a very sensible convention: The intersection or product of the empty
collection of ideas should be taken to equal the unit ideal
[latex](1)[/latex] while the sum of the empty collection should be the zero
ideal [latex](0)[/latex].
If that bothers you, insert “proper” in the statement of 1.20 after “For
all”.
I promise that I will not try to catch you out with such things!
PS Apologoes to Henrique for misspelling his name earlier. I hope I have
it right now.
MA3G6 Commutative Algebra
MA3G6 Commutative Algebra
empty intersections of ideals
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