Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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).


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 13B25, 13F05, 13F20, 11C08

Retrieve articles in all journals with MSC (1991): 13B25, 13F05, 13F20, 11C08


Additional Information

Sophie Frisch
Affiliation: Institut für Mathematik C, Technische Universität Graz, Kopernikusgasse 24, A-8010 Graz, Austria
Email: frisch@blah.math.tu-graz.ac.at

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03442-9
PII: S 0002-9939(96)03442-9
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