Tell me more ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
up vote 1 down vote favorite

Let $M$ be a flat $A$-module, and $N$ a $A$-module isomorphic to $M$, what can we say about the flatness of $N$?

share|improve this question
3  
$N$ is flat? Or what do you want to hear? – martini Mar 27 '12 at 18:56
why is $N$ flat? – Jr. Mar 27 '12 at 19:09
2  
If $M\cong N$ as $A$-modules, then for any $A$-module $P$, $P\otimes_A M\cong P\otimes_A N$. – Rand al'Thor Mar 27 '12 at 19:24
2  
Dear 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. – Georges Elencwajg Mar 27 '12 at 21:39
Dear Georges , is there a formal proof of your statement? I mean, only using abstract category theory, does one could reach that conclusion? – Jr. Mar 27 '12 at 23:12
show 1 more comment

Know someone who can answer? Share a link to this question via email, Google+, Twitter, or Facebook.

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.