Bhargava Rings Over Subsets

  • I. Al-Rasasi
  • L. IzelgueEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 228)


Let D be an integral domain with quotient field K and let E be any nonempty subset of K. The Bhargava ring over E at \(x\in D\) is defined by \(\mathbb {B}_x(E,D):=\{f\in K[X]\mid f(xX+e)\in D[X], \ \forall e\in E\}\). This ring is a subring of the ring of integer-valued polynomials over E. This paper studies \(\mathbb {B}_x(E,D)\) for an arbitrary domain D. we provide information about its localizations and transfer properties, describe its prime ideal structure, and calculate its Krull and valuative dimensions.


Integer-valued polynomial Bhargava ring Prime ideal Localization Residue field Krull dimension Valuative dimension 


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Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsKing Fahd University of Petroleum and MineralsDhahranKingdom of Saudi Arabia
  2. 2.Department of Mathematics, Faculty of Sciences SemlaliaCadi Ayyad UniversityMarrakechMorocco

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