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TitleCurves and coherent Prüfer rings
Author(s) Thierry Coquand, H. Lombardi, Claude Quitté
TypeArticle in Journal
AbstractWe show, in constructive mathematics, that if k is a discrete field and f an arbitrary polynomial in k [ x , y ] then the localisation R_f_y is always a semihereditary ring, where R denotes the ring k [ x , y ] quotiented by f . An important corollary is that R is semiherditary whenever 1 = 〈 f , f_x , f_y 〉 . This can be seen as the constructive content of the theorem saying that if moreover R is a domain, then it is Dedekind.
KeywordsSemihereditary ring, pp-ring, Prüfer ring, Smooth curve, Constructive mathematics, Generalized Hasse derivatives
ISSN0747-7171
URL http://www.sciencedirect.com/science/article/pii/S0747717110000969
LanguageEnglish
JournalJournal of Symbolic Computation
Volume45
Number12
Pages1378 - 1390
Year2010
NoteMEGA’2009
Edition0
Translation No
Refereed No
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