Let D be an integral domain with quotient field K. We consider the ring of integer-valued polynomials over D, namely, Int(D) ∶= {f ∈ K[X]; f(D) ⊆ D}. In this paper we investigate when Int(D) has essentialtype properties. In particular, we give a complete characterization of when Int(D)is locally essential, locally PvMD, locally UFD, locally GCD, Krull-type or generalized Krull.
Tamoussit, A., Tartarone, F. (2023). Essential properties for rings of integer-valued polynomials. NEW YORK JOURNAL OF MATHEMATICS, 29, 467-487.
Essential properties for rings of integer-valued polynomials
Tartarone F.
Writing – Review & Editing
2023-01-01
Abstract
Let D be an integral domain with quotient field K. We consider the ring of integer-valued polynomials over D, namely, Int(D) ∶= {f ∈ K[X]; f(D) ⊆ D}. In this paper we investigate when Int(D) has essentialtype properties. In particular, we give a complete characterization of when Int(D)is locally essential, locally PvMD, locally UFD, locally GCD, Krull-type or generalized Krull.File in questo prodotto:
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