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<p>We say <i>R</i> ⊆ <i>S</i> is pinched at some intermediate ring <i>R</i><sub>0</sub>, where <i>R</i> ⊂ <i>R</i><sub>0</sub> ⊂ <i>S</i>, if each intermediate ring between <i>R</i> and <i>S</i> is comparable to <i>R</i><sub>0</sub> under inclusion. A new characterization of Prüfer extensions in terms of maximal excluding domains is given. We also characterize minimal extensions of a Prüfer domain and prove that no extension of a one-dimensional Prüfer domain can be pinched, and thereby extending old results of Gilbert on <i>λ</i>-extensions. Next, we show that a proper finite Galois extension is pinched if and only if the Galois group is cyclic of prime power order. Further, the preservation of comparability of the integral closure and that of <i>λ</i>-finiteness in pullbacks is also studied.</p>

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A note on pinched extensions

  • 期刊论文

  • 发表日期：

    2026年3月2日

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  • Mandeep Singh,
  • Ravinder Singh

摘要

We say R ⊆ S is pinched at some intermediate ring R0, where R ⊂ R0 ⊂ S, if each intermediate ring between R and S is comparable to R0 under inclusion. A new characterization of Prüfer extensions in terms of maximal excluding domains is given. We also characterize minimal extensions of a Prüfer domain and prove that no extension of a one-dimensional Prüfer domain can be pinched, and thereby extending old results of Gilbert on λ-extensions. Next, we show that a proper finite Galois extension is pinched if and only if the Galois group is cyclic of prime power order. Further, the preservation of comparability of the integral closure and that of λ-finiteness in pullbacks is also studied.