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 mis-spelling his name earlier. I hope I have it right now.