Projective Dimensions of Ideals of Prufer Domains
A Prüfer domain has all of its finitely generated ideals projective. Countably but not finitely generated ideals must be of projective dimension 1. A standard argument due to Auslander gives an upper bound for the projective dimension of an ideal I. If I is Nk-generated, then I has projective dimension ≆ = k+1. Here we look at how one might get the reverse inequality.
KeywordsExact Sequence Intersection Property Standard Argument Projective Module Projective Dimension
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