Abstract
Let D be an integral domain with quotient field K, E a subset of K and X an indeterminate over K. The set of integer–valued polynomials on E is defined by \(\mathrm {Int}(E, D) = \{f \in K[X]:f (E) \subseteq D\}\). Clearly, \(\mathrm {Int}(E, D\)) is a subring of K[X] and \(\mathrm {Int}(D, D) = \mathrm {Int}(D)\), the ring of integer–valued polynomials over D. In this paper, we investigate some conditions under which \(\mathrm {Int}(E,D)\) is locally free, or at least flat, as a D–module. Particularly, we are interested in domains that are locally essential with subsets E residually cofinite.
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Izelgue, L., Tamoussit, A. (2018). When Is \(\mathrm {Int}(E,D)\) a Locally Free D–Module. In: Badawi, A., Vedadi, M., Yassemi, S., Yousefian Darani, A. (eds) Homological and Combinatorial Methods in Algebra. SAA 2016. Springer Proceedings in Mathematics & Statistics, vol 228. Springer, Cham. https://doi.org/10.1007/978-3-319-74195-6_10
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