A simple extension of a von Neumann regular ring
Kyoto Journal of Mathematics, 1985 Let \(R\) be a commutative von Neumann regular ring and \(R[\alpha]\) be a reduced simple extension of \(R\), i.e. \(R[\alpha]\cong R[x]/I\) with a semi- prime ideal \(I \leq R[x]\) such that \(R\cap I=\{0\}\). The author gives conditions on \(I\) for \(R[\alpha]\) to be quasi-regular. E.g.
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