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Finite Intersections of Prüfer Overrings

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Advances in Commutative Algebra

Part of the book series: Trends in Mathematics ((TM))

Abstract

This article is motivated by the open question of whether every integrally closed domain is an intersection of finitely many Prüfer overrings. We survey the work of Dan Anderson and David Anderson on this and related questions, and we show that an integrally closed domain that is a finitely generated algebra over a Dedekind domain or a field is a finite intersection of Dedekind overrings. We also discuss how recent work on the intersections of valuation rings has implications for this question.

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Acknowledgements

I thank the referee for the helpful comments.

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Authors and Affiliations

  1. New Mexico State University, Las Cruces, NM, 88003-8001, USA

    Bruce Olberding

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  1. Bruce Olberding
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Correspondence to Bruce Olberding .

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Editors and Affiliations

  1. Department of Mathematics and Statistics, American University of Sharjah, Sharjah, United Arab Emirates

    Ayman Badawi

  2. Department of Mathematical Sciences, Clemson University, Clemson, SC, USA

    Jim Coykendall

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Olberding, B. (2019). Finite Intersections of Prüfer Overrings. In: Badawi, A., Coykendall, J. (eds) Advances in Commutative Algebra. Trends in Mathematics. Birkhäuser, Singapore. https://doi.org/10.1007/978-981-13-7028-1_5

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