## when two ring A,B are flat, then are they isomorphic? [closed]

Let ring A and B be a flat over k[t]/(t^{2}).

if there are morphism f from A to B then, f should be isomorphism?

if so, why?

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There is no reason that $f$ should be an isomorphism. – Kevin Buzzard May 16 2011 at 18:01
It's hard to answer this question because nothing like this is true. For example, $k[t]/(t^2)$ is flat over itself and $k[t, x]/(t^2)$ is also flat over $k[t]/(t^2)$, and there are plenty of maps between them. Could you give us some context about why you think this? – David Speyer May 16 2011 at 19:10
Since your question is about to get closed: I suggest that you follow David Speyer's advice, edit your question to clarify what it is you think is true, and then use the 'flag' option to contact a moderator asking if the question can be re-opened. – Yemon Choi May 16 2011 at 22:27