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Multiplicative Ideal Theory and Factorization Theory pp 219–231Cite as

Prüfer Domains of Integer-Valued Polynomials

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 170))

Abstract

Let D be an integral domain with quotient field K. The ring \(\mathrm {Int}(D) = \{f(x) \ \Vert \ f(D) \subseteq D \}\) has been studied as a ring for more than forty years. A major topic of interest during that time has been the question of when the construction yields a Prüfer domain. The principal question has been resolved, but interesting generalizations are still being worked on. This is a survey paper that traces the history of study of integer-valued polynomial rings with a focus on when they are Prüfer domains .

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Author information

Authors and Affiliations

  1. Department of Mathematics, The Ohio State University–Newark, Newark, OH, 43055, USA

    K. Alan Loper

  2. Department of Mathematics, The Ohio State University, Columbus, OH, 43210, USA

    Mark Syvuk

Authors
  1. K. Alan Loper
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  2. Mark Syvuk
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Correspondence to K. Alan Loper .

Editor information

Editors and Affiliations

  1. Dept of Math & Stat, Sam Houston State University, Huntsville, Texas, USA

    Scott Chapman

  2. Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre, Rome, Italy

    Marco Fontana

  3. Institut für Mathematik und Wissenschaftliches Rechnen, Universität Graz, Graz, Austria

    Alfred Geroldinger

  4. Dept. Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico, USA

    Bruce Olberding

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Loper, K.A., Syvuk, M. (2016). Prüfer Domains of Integer-Valued Polynomials. In: Chapman, S., Fontana, M., Geroldinger, A., Olberding, B. (eds) Multiplicative Ideal Theory and Factorization Theory. Springer Proceedings in Mathematics & Statistics, vol 170. Springer, Cham. https://doi.org/10.1007/978-3-319-38855-7_9

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