New York Journal of Mathematics
Volume 29 (2023), 467-487


Ali Tamoussit and Francesca Tartarone

Essential properties for rings of integer-valued polynomials

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Published: May 3, 2023.
Keywords: Integer-valued polynomials, essential domain, PvMD.
Subject [2010]: 13A15, 13A18, 13B30, 13F05, 13F20.

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 essential-type 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.


The second author was partially supported by GNSAGA of Istituto Nazionale di Alta Matematica.

Author information

Ali Tamoussit
Department of Mathematics
The Regional Center for Education and Training Professions Souss Massa
Inezgane, Morocco, and
Laboratory of Mathematics and Applications (LMA)
Faculty of Sciences
Ibn Zohr University, Agadir, Morocco


Francesca Tartarone
Dipartimento di Matematica e Fisica
Universitá degli Studi Roma Tre
00146 Roma, Italy