Answer to Question #25767 in Abstract Algebra for john.george.milnor

Question #25767
Let E = End(Vk) where V is a right vector space over the division ring k., and let R ⊆ E be a dense subring. Deduce that the set S = {a ∈ R : rank(a) < ∞} is a von Neumann regular ring (possibly without identity).
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