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Radical of a ring
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===The von Neumann regular radical=== A [[von Neumann regular ring]] is a ring ''A'' (possibly non-commutative without multiplicative identity) such that for every ''a'' there is some ''b'' with ''a'' = ''aba''. The von Neumann regular rings form a radical class. It contains every [[matrix ring]] over a [[division algebra]], but contains no nil rings.
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