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- W4298068849 abstract "Let D be an integral domain with quotient field K. For any set X, the ring Int(D^X) of integer-valued polynomials on D^X is the set of all polynomials f in K[X] such that f(D^X) is a subset of D. Using the t-closure operation on fractional ideals, we find for any set X a D-algebra presentation of Int(D^X)$ by generators and relations for a large class of domains D, including any unique factorization domain D, and more generally any Krull domain D such that Int(D) has a regular basis, that is, a D-module basis consisting of exactly one polynomial of each degree. As a corollary we find for all such domains D an intrinsic characterization of the D-algebras that are isomorphic to a quotient of Int(D^X) for some set X. We also generalize the well-known result that a Krull domain D has a regular basis if and only if the Polya-Ostrowski group of D (that is, the subgroup of the class group of D generated by the images of the factorial ideals of D) is trivial, if and only if the product of the height one prime ideals of finite norm q is principal for every q." @default.
- W4298068849 created "2022-10-01" @default.
- W4298068849 creator A5046566668 @default.
- W4298068849 date "2011-09-18" @default.
- W4298068849 modified "2023-09-28" @default.
- W4298068849 title "Presentations and module bases of integer-valued polynomial rings" @default.
- W4298068849 doi "https://doi.org/10.48550/arxiv.1109.3921" @default.
- W4298068849 hasPublicationYear "2011" @default.
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