2012/04/18 by Bruce Olberding, Olberding, Bruce
Mathematics · #13B22 #13B35 #13E05 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13B22 #msc:13B35 #msc:13E05
paper · pdf · doi:10.48550/arxiv.1204.3962
29 pages. arXiv admin note: substantial text overlap with arXiv:1009.3957
arxiv created 2012/04/18 · arxiv updated 2012/04/19
Idealization of a module K over a commutative ring S produces a ring having K as an ideal, all of whose elements are nilpotent. We develop a method that under suitable field-theoretic conditions produces from an S-module K and derivation D:S→ K a subring R of S that behaves like the idealization of K but is such that when S is a domain, so is R. The ring S is contained in the normalization of R but is finite over R only when R = S. We determine conditions under which R is Noetherian, Cohen-Macaulay, Gorenstein, a complete intersection or a hypersurface. When R is local, then its \bf m-adic completion is the idealization of the \bf m-adic completions of S and K.