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On the Ideal Theory of the KroneckerFunction Ring and the Domain D(X)

Published online by Cambridge University Press:  20 November 2018

Jimmy T. Arnold
Jimmy T. Arnold*
Affiliation:
Florida State University, Tallahassee, Florida
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Let D be an integrally closed domain with identity having quotient field L. If {Vα} is the set of valuation overrings of D and if A is an ideal of D, then à = ∪ αAVα is an ideal of D called the completion of A. If X is an indeterminate over D and f ∈ D[X], then we denote by Af the ideal of D generated by the coefficients of f. The Kronecker function ring DK of D is defined by DK = {f/g| f, g ∈ D[X], Ãf ⊆ Ag} (4, p. 558); and the domain D(X) is defined by D(X) = {f/g| f, g ∈ D[X], Ag = D} (5, p. 17). In this paper we wish to relate the ideal theory of D to that of DK and D(X) for the case in which D is a Prüfer domain, a Dedekind domain, or an almost Dedekind domain.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 558 - 563
Copyright
Copyright © Canadian Mathematical Society 1969

References

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