Let D be a domain with quotient 7eld K and let Int(D) be the ring of integer-valued polynomials {f ∈ K[X ] | f(D) ⊆ D}. We give conditions on D so that the ring Int(D) is a Strong Mori domain. In particular, we give a complete characterization in the case that the conductor (D :D) is nonzero, where D is the integral closure of D. We also show that when D is quasilocal with Int(D) =D[X] or D is Noetherian, Int(D) is a Strong Mori domain if and only if Int(D) is Noetherian.
PARK M., H., Tartarone, F. (2004). Strong Mori and Noetherian properties of integer-valued polynomial rings. JOURNAL OF PURE AND APPLIED ALGEBRA, 186 N.3, 297-309-309 [10.1016/S0022-4049(03)00131-2].
Strong Mori and Noetherian properties of integer-valued polynomial rings
TARTARONE, FRANCESCA
2004-01-01
Abstract
Let D be a domain with quotient 7eld K and let Int(D) be the ring of integer-valued polynomials {f ∈ K[X ] | f(D) ⊆ D}. We give conditions on D so that the ring Int(D) is a Strong Mori domain. In particular, we give a complete characterization in the case that the conductor (D :D) is nonzero, where D is the integral closure of D. We also show that when D is quasilocal with Int(D) =D[X] or D is Noetherian, Int(D) is a Strong Mori domain if and only if Int(D) is Noetherian.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
