Example of noncommutative ring in which all nonzero elements are invertible.
I was thinking along Matrices in $(2,\mathbb Z$), but some nonzero matrices are not invertible.
Can someone provide me with an example?
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1Hamilton's Quaternions: https://en.wikipedia.org/wiki/Quaternion – DonAntonio Mar 13 '16 at 12:53
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You can indeed "think along matrices", too, by representing the quaternion algebra by complex $2\times 2$ matrices. – Dietrich Burde Mar 13 '16 at 14:48