The integral-closedness criterion for integer-valued polynomial rings on algebras
The integral-closedness criterion for integer-valued polynomial rings on algebras
Let be an ADDB-domain. Let be a -algebra that is torsion-free and finitely generated as a -module, with , and let . Thus and satisfy the hypotheses of the main theorem.
Integral-closedness criterion. If is integrally closed, then is Prüfer.
The theorem preceding this conjecture gives several equivalent conditions for to be Prüfer, including its equality with and the condition . The conjecture asks whether integral closedness alone is sufficient in the general ADDB-domain setting; the full resolution remains open.
Sources & referencesView supporting material
Primary source
Giulio Peruginelli and Nicholas J. Werner, “A classification of Prufer domains of integer-valued polynomials on algebras”, arXiv:2509.09243 (2026).
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