Let I be a principal ideal of a domain R, say I = aR. Show that and that I is invertible.
The inverse of I is the set of , where K is the quotient field of R.
I think I have the solution:
pick j to be an element of , then , so we have for some r in R, and i in I. Let i = am, for some elements m in R.
So we have j(am) = r
is an element of R, so
Well, now I have to show that is a subseteq of of ...