For an integral domain D with quotient eld K, the ring of integer-valued polyno mials over D, denoted by Int(D), consists of all polynomials f in K[X] such that f(D) ⊆ D. In this paper, we collect results on the transfer of some essential-like properties between D and Int(D). Particular attention is given to the essentiality of integer-valued polynomial rings over valuation domains.
Tamoussit, A., Tartarone, F. (2025). Essential-like properties for integer-valued polynomial rings: a survey with a note on valuation domains. In Recent progress in ring and factorization theory (pp.417-428). Springer [10.1007/978-3-031-75326-8\_19].
Essential-like properties for integer-valued polynomial rings: a survey with a note on valuation domains
Francesca Tartarone
2025-01-01
Abstract
For an integral domain D with quotient eld K, the ring of integer-valued polyno mials over D, denoted by Int(D), consists of all polynomials f in K[X] such that f(D) ⊆ D. In this paper, we collect results on the transfer of some essential-like properties between D and Int(D). Particular attention is given to the essentiality of integer-valued polynomial rings over valuation domains.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
