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For an integral domain D with quotient field K, the ring of integer-valued polynomials over D, denoted by \(\textrm{Int}(D)\) , consists of all polynomials f in K[X] such that \(f(D)\subseteq D\) . In this paper, we collect results on the transfer of some essential-like properties between D and \(\textrm{Int}(D)\) . Particular attention is given to the essentiality of integer-valued polynomial rings over valuation domains.

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Essential-Like Properties for Integer-Valued Polynomial Rings: A Survey with a Note on Valuation Domains

  • 会议论文

  • 发表日期：

    2025年

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  • Ali Tamoussit,
  • Francesca Tartarone

摘要

For an integral domain D with quotient field K, the ring of integer-valued polynomials over D, denoted by \(\textrm{Int}(D)\) , consists of all polynomials f in K[X] such that \(f(D)\subseteq D\) . In this paper, we collect results on the transfer of some essential-like properties between D and \(\textrm{Int}(D)\) . Particular attention is given to the essentiality of integer-valued polynomial rings over valuation domains.