Let D be a Krull domain with quotient eld K. We study the class group of the integer-valued polynomial ring over D, Int(D) :=ff 2 K[X ]; f(D)Dg. In particular, we give necessary and sucient conditions on D for the class group of Int(D) to be generated by the classes of the t-invertible t-prime ideals and, in this case, we describe its generators. A case of particular interest is when D is a UFD. We also characterize Krull domains D for which Int(D) is a GCD-domain.
Gabelli, S., Tartarone, F. (2000). On the class group of integer-valued polynomial rings over Krull domains. JOURNAL OF PURE AND APPLIED ALGEBRA, 149, 47-67 [10.1016/S0022-4049(98)00159-5].
On the class group of integer-valued polynomial rings over Krull domains
TARTARONE, FRANCESCA
2000-01-01
Abstract
Let D be a Krull domain with quotient eld K. We study the class group of the integer-valued polynomial ring over D, Int(D) :=ff 2 K[X ]; f(D)Dg. In particular, we give necessary and sucient conditions on D for the class group of Int(D) to be generated by the classes of the t-invertible t-prime ideals and, in this case, we describe its generators. A case of particular interest is when D is a UFD. We also characterize Krull domains D for which Int(D) is a GCD-domain.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
