Some relationship between anti-integral extensions of Noetherian domains (Q2709729)

The authors study extensions of a Noetherian integral domain \(R\) of the form \(R[\alpha]\) and \(R[\alpha,\alpha^{-1}]\), where \(\alpha\) is an anti-integral element over \(R\). For example, under suitable assumptions on the anti-integral elements \(\alpha,\beta\) and \(\gamma\), the authors prove that \(R[\beta]\) is flat over \(R\) iff \(R[\gamma]\) is flat over \(R\) (theorem 9 (1)). They also study certain ideals related to anti-integral elements.