A classification of all

such that is a Prüfer domain

Author:
K. Alan Loper

Journal:
Proc. Amer. Math. Soc. **126** (1998), 657-660

MSC (1991):
Primary 13F05, 13F20; Secondary 13B25, 11C08

DOI:
https://doi.org/10.1090/S0002-9939-98-04459-1

MathSciNet review:
1459137

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be an integral domain with quotient field . The ring of integer-valued polynomials over is defined by . It is known that if is a Prüfer domain, then is an almost Dedekind domain with all residue fields finite. This condition is necessary and sufficient if is Noetherian, but has been shown to not be sufficient if is not Noetherian. Several authors have come close to a complete characterization by imposing bounds on orders of residue fields of and on normalized values of particular elements of . In this note we give a double-boundedness condition which provides a complete charaterization of all integral domains such that is a Prüfer domain.

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Additional Information

**K. Alan Loper**

Affiliation:
Department of Mathematics, Ohio State University-Newark, Newark, Ohio 43055

Email:
lopera@math.ohio-state.edu

DOI:
https://doi.org/10.1090/S0002-9939-98-04459-1

Received by editor(s):
August 26, 1996

Communicated by:
Wolmer V. Vasconcelos

Article copyright:
© Copyright 1998
American Mathematical Society