A generalization of Kronecker function rings and Nagata rings
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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.
© Walter de Gruyter
Articles in the same Issue
- On the simple connectedness of certain subsets of buildings
- A generalization of Kronecker function rings and Nagata rings
- Cotilting and tilting modules over Prüfer domains
- Derivations of multi-loop algebras
- Injective and colon properties of ideals in integral domains
- A Lewis Correspondence for submodular groups
- Spreads of PG(3, q) and ovoids of polar spaces
- Meromorphic continuation of multivariable Euler products
Articles in the same Issue
- On the simple connectedness of certain subsets of buildings
- A generalization of Kronecker function rings and Nagata rings
- Cotilting and tilting modules over Prüfer domains
- Derivations of multi-loop algebras
- Injective and colon properties of ideals in integral domains
- A Lewis Correspondence for submodular groups
- Spreads of PG(3, q) and ovoids of polar spaces
- Meromorphic continuation of multivariable Euler products
