An anonymous student asked > In the Commutative Algebra Notes, should prop 1.20 be for all ideals > excluding R, as no prime ideals contain R but r(R)=R? > > and my reply is > The clever answer is to say that when there are no primes > containing (as you correctly say) and that the empty intersection is > , just as an empty product is always taken to be 1. That way you > don't need to make a special case. If you don't like that then > just assume , but I think it is more elegant to keep in the > special case with that convention! > >