William J. Heinzer

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Let I be a proper nonnilpotent ideal in a local (Noetherian) ring (R,M) and let J be a reduction of I; that is, J ⊆ I and JIn = In+1 for some nonnegative integer n. We prove that there exists a finite free local unramified extension ring S of R such that the ideal IS has a minimal reduction K ⊆ JS with the property that the number of elements in a minimal(More)
Let I be an m-primary ideal of a Noetherian local ring (R,m). We consider the Gorenstein and complete intersection properties of the associated graded ring G(I) and the fiber cone F (I) of I as reflected in their defining ideals as homomorphic images of polynomial rings over R/I and R/m respectively. In case all the higher conormal modules of I are free(More)
C ↪→ D1 := k[x] [[y/x]] ↪→ · · · ↪→ Dn := k[x] [[y/x]] ↪→ · · · ↪→ E. (2) With regard to Equation 2, for n a positive integer, the map C ↪→ Dn is not flat, but Dn ↪→ E is a localization followed by an adic completion of a Noetherian ring and therefore is flat. We discuss the spectra of these rings and consider the maps induced on the spectra by the(More)