Riassunto
Si dimostra che un dominioS è un anello di funzioni di Kronecker (in una variabile) se e soltanto seS è integralmente chiuso, il suo campo dei quozienti è della formaF(Y), doveY è trascendente suF, il campo dei quozienti diS∩F èF, e ogni sopraanello di volutazioneW diS coincide con l'estensione banale diW∩F. Inoltre, vengono classificati tutti i sottoanelli di funzioni di Kronecker diK(X), per vari importanti casi del campoK.
Summary
We show that an integral domainS is a Kronecker function ring if and only ifS is integrally closed, its field of quotients isF(Y), whereF is a field such that the quotient field ofS∩F is exactlyF, Y is transcendental overF and every valuation overringW ofS coincides with the trivial extension ofW∩F. Furthermore, we classify all the Kronecker function rings, subrings ofK(X), for several important types of fieldsK.
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This work is partially supported by a NATO Collaborative Research Grant.
Supported in part by Università di Roma «La Sapienza» and a Faculty Development Grant from the University of Tennessee.
Supported in part by Università di Roma «La Sapienza» and University of Tennessee.
Work done under the auspices of G.N.S.A.G.A. of the Consiglio Nazionale delle Ricerche.
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Anderson, D.F., Dobbs, D.E. & Fontana, M. Characterizing Kronecker function rings. Ann. Univ. Ferrara 36, 1–13 (1990). https://doi.org/10.1007/BF02837203
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DOI: https://doi.org/10.1007/BF02837203