Let $M$ be a flat $A$-module, and $N$ a $A$-module isomorphic to $M$, what can we say about the flatness of $N$?
Module isomorphic to a flat module
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commutative-algebra
modules
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4$N$ is flat? Or what do you want to hear? – 2012-03-27
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0why is $N$ flat? – 2012-03-27
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4If $M\cong N$ as $A$-modules, then for any $A$-module $P$, $P\otimes_A M\cong P\otimes_A N$. – 2012-03-27
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5Dear Jr., here is a meta-rule for you. Whenever mathematicians define a property P that some objects in a category may or may not have, you can be sure that if an object has property P, then any isomorphic object also has property P. – 2012-03-27
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0Dear Georges , is there a formal proof of your statement? I mean, only using abstract category theory, does one could reach that conclusion? – 2012-03-27
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0@Randal'Thor Thanks! – 2012-03-27
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0@Randal'Thor Please consider converting your comment into an answer, so that this question gets removed from the [unanswered tab](http://meta.math.stackexchange.com/q/3138). If you do so, it is helpful to post it to [this chat room](http://chat.stackexchange.com/rooms/9141) to make people aware of it (and attract some upvotes). For further reading upon the issue of too many unanswered questions, see [here](http://meta.stackexchange.com/q/143113), [here](http://meta.math.stackexchange.com/q/1148) or [here](http://meta.math.stackexchange.com/a/9868). – 2013-06-13