Can two non-isomorphic local domains have isomorphic quotient field and residue field?

Question

Suppose $R,R'$ are non-isomorphic local domains with maximal ideals $\mathfrak{m,m'}$. Can they have isomorphic quotient field and residue field?

You could take $k[[t^2,t^3]] \subseteq k[[t]]$. – Youngsu Oct 23 '13 at 07:57 — Youngsu, Oct 23 '13 at 07:57
@Youngsu: Nice. This is an answer, not a comment. – Martin Brandenburg Oct 23 '13 at 08:05 — Martin Brandenburg, Oct 23 '13 at 08:05

score 2 · Accepted Answer · answered Oct 27 '13 at 14:31

2

This is the comment posted by Youngsu: Take $R=k[[t^2,t^3]]\subset R'=k[[t]]$.

answered Oct 27 '13 at 14:31

1 Answers1