Proc. Amer. Math. Soc. 124 (1996) 3595-3604 [MR 97b:13012, Zb 970.00200]

# Integer-Valued Polynomials on Krull Rings

Abstract:
Let R be a subring of a Krull ring S such that for every ideal Q
of finite index in R that is the restriction of a prime ideal of
height 1 of S, the localization R_Q is a valuation ring.
Using sequences of ring elements with nice distribution properties
with respect to residue classes of ideals of S (later called
P-orderings), we construct polynomials in R[x] that map R into the
maximal possible (for a monic polynomial of fixed degree) power of PS_P,
for all height 1 prime ideals P of 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).

1991 Mathematics Subject Classification: Primary 13B25, 13F05;
Secondary 13F20, 11C08.

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