Recent content by Mathsgirl

I can see that R must be all integers plus some rationals, an example of this could be {a*2^(-b): for an integer a and natural number b}, but I'm not sure how to write down a more general subring? If I consider an ideal I of R, I need to show that it is principal, so of the form aR for some a...

Homework Statement Prove that R is a PID (principal ideal domain) when R is a ring such that Z \subset R \subset Q (Z=integers, Q=rationals) Homework Equations The Attempt at a Solution So I'm not really sure how to start this problem. I know that a principal ideal domain is an...

Oh that makes more sense. I think I need to say something like you can always fit a smaller ball inside an open ball. I remember in real analysis I showed for a non-empty bounded above set E and epsilon >0, there exists an x in E such that supE - epsilon < x \leq sup E. Is it something...

Homework Statement R>0, let K be a closed subset of C such that K \subset BR(0) (so K is compact). Show that there exists 0 < r < R such that K\subset Br(0). Homework Equations The Attempt at a Solution Can I write BR(0) = {x\inC : d(x,0) \leqR}? I know that a compact set is closed and...