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Sep 11, 2012 at 23:01 comment added user2013 Thank you all for the comments. I added what I menat by deformation. The deformation argument may not need commutativity of the base ring as you pointed out.
Sep 11, 2012 at 22:58 history edited user2013 CC BY-SA 3.0
some information added
Sep 11, 2012 at 13:30 comment added Bugs Bunny I am with Mariano on this one. Commutativity is not really an issue if the deformations are usual.
Sep 11, 2012 at 6:57 comment added Amin The references I know for deformations of modules are work of Waldmann and Burstyn, and also some previous work of Weinstein (as collaborator to other authors), and there indeed there was no need that the base ring be commutative. As M. Suarez-Alvarez said though, this is quite similar to standard things (like first explained by Gerstenhaber I think), so you should really explain if you're using a particular definition of deformation.
Sep 11, 2012 at 5:18 comment added Mariano Suárez-Álvarez (I am asking because the simplest arguments I know to show the claims you make about $Ext^1$ and $Ext^2$ work excatly the same for commutative and non-commutative rings... so there must be something different)
Sep 11, 2012 at 5:17 comment added Mariano Suárez-Álvarez Can you tell us exactly what you mean by "deformation"?
Sep 11, 2012 at 4:51 comment added user2013 $E$ must be $M$. Thank you for pointing this out.
Sep 11, 2012 at 4:51 history edited user2013 CC BY-SA 3.0
typos corrected
Sep 10, 2012 at 16:52 comment added Qiaochu Yuan What is $E$ here?
Sep 10, 2012 at 9:33 history asked user2013 CC BY-SA 3.0