Relative polynomial closure and monadically Krull monoids of integer-valued polynomials
Abstract
Let D be a Krull domain and Int(D) the ring of integer-valued polynomials on D. For any f in Int(D), we explicitly construct a divisor homomorphism from [f], the divisor-closed submonoid of Int(D) generated by f, to a finite sum of copies of (N_0,+). This implies that [f] is a Krull monoid. For V a discrete valuation domain, we give explicit divisor theories of various submonoids of Int(V). In the process, we modify the concept of polynomial closure in such a way that every subset of D has a finite polynomially dense subset. The results generalize to Int(S,V), the ring of integer-valued polynomials on a subset, provided S doesn't have isolated points in v-adic topology.
Keywords
Cite
@article{arxiv.1409.1111,
title = {Relative polynomial closure and monadically Krull monoids of integer-valued polynomials},
author = {Sophie Frisch},
journal= {arXiv preprint arXiv:1409.1111},
year = {2016}
}
Comments
12 pages; v.2 contains corrections, in that some necessary conditions on those subsets S, for which we consider integer-valued polynomials on subsets, are imposed