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When Is \(\mathrm {Int}(E,D)\) a Locally Free D–Module

  • Lahoucine Izelgue
  • Ali TamoussitEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 228)

Abstract

Let D be an integral domain with quotient field K, E a subset of K and X an indeterminate over K. The set of integer–valued polynomials on E is defined by \(\mathrm {Int}(E, D) = \{f \in K[X]:f (E) \subseteq D\}\). Clearly, \(\mathrm {Int}(E, D\)) is a subring of K[X] and \(\mathrm {Int}(D, D) = \mathrm {Int}(D)\), the ring of integer–valued polynomials over D. In this paper, we investigate some conditions under which \(\mathrm {Int}(E,D)\) is locally free, or at least flat, as a D–module. Particularly, we are interested in domains that are locally essential with subsets E residually cofinite.

Keywords

Integer–valued polynomials Flat modules Locally free modules Residue field Locally essential domains 

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Sciences SemlaliaCadi Ayyad UniversityMarrakechMorocco

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