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A generalization of Kronecker function rings and Nagata rings

A generalization of Kronecker function rings and Nagata rings Let D be an integral domain with quotient field K . The Nagata ring D ( X ) and the Kronecker function ring Kr( D ) are both subrings of the field of rational functions K ( X ) containing as a subring the ring D X of polynomials in the variable X . Both of these function rings have been extensively studied and generalized. The principal interest in these two extensions of D lies in the reflection of various algebraic and spectral properties of D and Spec( D ) in algebraic and spectral properties of the function rings. Despite the obvious similarities in definitions and properties, these two kinds of domains of rational functions have been classically treated independently, when D is not a Prüfer domain. The purpose of this note is to study two different unified approaches to the Nagata rings and the Kronecker function rings, which yield these rings and their classical generalizations as special cases. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

A generalization of Kronecker function rings and Nagata rings

Forum Mathematicum , Volume 19 (6) – Nov 20, 2007

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References (40)

Publisher
de Gruyter
Copyright
© Walter de Gruyter
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/FORUM.2007.038
Publisher site
See Article on Publisher Site

Abstract

Let D be an integral domain with quotient field K . The Nagata ring D ( X ) and the Kronecker function ring Kr( D ) are both subrings of the field of rational functions K ( X ) containing as a subring the ring D X of polynomials in the variable X . Both of these function rings have been extensively studied and generalized. The principal interest in these two extensions of D lies in the reflection of various algebraic and spectral properties of D and Spec( D ) in algebraic and spectral properties of the function rings. Despite the obvious similarities in definitions and properties, these two kinds of domains of rational functions have been classically treated independently, when D is not a Prüfer domain. The purpose of this note is to study two different unified approaches to the Nagata rings and the Kronecker function rings, which yield these rings and their classical generalizations as special cases.

Journal

Forum Mathematicumde Gruyter

Published: Nov 20, 2007

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