Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10325481 | Journal of Symbolic Computation | 2010 | 13 Pages |
Abstract
We show, in constructive mathematics, that if k is a discrete field and f an arbitrary polynomial in k[x,y] then the localisation Rfy 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=ãf,fx,fyã. This can be seen as the constructive content of the theorem saying that if moreover R is a domain, then it is Dedekind.
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Authors
Thierry Coquand, Henri Lombardi, Claude Quitté,