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I included a bunch of equivalent definitions of ’von Neumann regular ring’, and a proof of what’s essentially Lemma 5 from von Neumann’s original paper. This clarifies the funny-looking equation .
My lemma and proof are not correctly formatted. Maybe someone could do that? I always have to look up how to do it.
I don’t know if it’s the best way but I just wrote \begin{lemma} \end{lemma} \begin{proof} \end{proof} and it works fine.
have replaced the broken link “[[Morita invariant]]
” by “invariant under Morita equivalences”
Changed
One can characterize commutative von Neumann rings as certain subrings of fields.
to
One can characterize commutative von Neumann rings as certain subrings of products of fields.
Von Neumann regular rings can have zero divisors, e.g. , so they are not all subrings of fields
Added reference
Anonymouse
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