I would use some help with following task:
Prove that when in ring R products xy and yx are invertible then elements x and y are also invertible.
Thanks in advance.
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What does it mean by definition that is invertible?
If you have the definition then you can use the fact that the multiplication is an associative operation.
It means that there exists (xy)^-1 so that (xy)^-1 * xy = 1
Originally Posted by rain1 It means that there exists (xy)^-1 so that (xy)^-1 * xy = 1 Yes, is invertible is there exists an unique such that .
Now, use the associtativity.
You mean like this? ? Thats all?
Last edited by rain1; March 24th 2013 at 11:38 AM.
Originally Posted by rain1 You mean like this? ? Thats all? In fact, what I mean is the following.
Suppose is invertible then there exists an unique such that . Since (here I use the associativity), we find that is invertible with as the inverse element.
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