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Pairs of integral domains with most of the intermediate rings PVD

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Abstract

Given a ring extension \(R \subset S\) of integral domains, it is shown that if each proper subring of S containing R is a PVD, then S is a PVD. As an application, we show that if each proper subring of S containing R is a valuation domain (resp., a DVR), then S is valuation domain (resp. S is the quotient field of R).

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Acknowledgments

The authors would like to thank the referee for many valuable suggestions.

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Author notes

  1. Noômen Jarboui

    Present address: Department of Mathematics, Faculty of Sciences, King Faisal University, P. O. Box 380, Al-hassa, 31982, Saudi Arabia

Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, University of Sfax, P. O. Box 1171, 3000, Sfax, Tunisia

    Noômen Jarboui & Salma Trabelsi

Authors
  1. Noômen Jarboui
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  2. Salma Trabelsi
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Correspondence to Noômen Jarboui.

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Communicated by Marco Fontana.

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Jarboui, N., Trabelsi, S. Pairs of integral domains with most of the intermediate rings PVD. Ricerche mat 66, 425–430 (2017). https://doi.org/10.1007/s11587-016-0310-z

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  • DOI: https://doi.org/10.1007/s11587-016-0310-z

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