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Integer-valued polynomials on Krull rings

Author: Sophie Frisch
Journal: Proc. Amer. Math. Soc. 124 (1996), 3595-3604
MSC (1991): Primary 13B25, 13F05; Secondary 13F20, 11C08
MathSciNet review: 1340386
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Abstract: If $R$ is a subring of a Krull ring $S$ such that $R_{Q}$ is a valuation ring for every finite index $Q=P\cap R$, $P$ in Spec$^{1}(S)$, we construct polynomials that map $R$ into the maximal possible (for a monic polynomial of fixed degree) power of $PS_{P}$, for all $P$ in Spec$^{1}(S)$ simultaneously. This gives a direct sum decomposition of Int$(R,S)$, the $S$-module of polynomials with coefficients in the quotient field of $S$ that map $R$ into $S$, and a criterion when Int$(R,S)$ has a regular basis (one consisting of 1 polynomial of each non-negative degree).

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Additional Information

Sophie Frisch
Affiliation: Institut für Mathematik C, Technische Universität Graz, Kopernikusgasse 24, A-8010 Graz, Austria

Received by editor(s): September 2, 1994
Received by editor(s) in revised form: May 1, 1995
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1996 American Mathematical Society

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