We prove that any affine ring R over a field k has full cosupport, ie, the cosupport of R is
equal to Spec R. Using this fact, we give a complete description of all terms in a minimal …

Given an affine algebra R= P/I, where P= K [x 1,…, xn] is a polynomial ring over a field K and
I is an ideal in P, we study re-embeddings of the affine scheme Spec (R), ie presentations …

Regular closure is an operation performed on submodules of arbitrary modules over a
commutative Noetherian ring. The regular closure contains the tight closure when both are …

Let R be an affine k-domain over the field k. The paper's main result is that if R admits a
nontrivial embedding in a polynomial ring K [s] for some field K containing k, then R can be …

Let $ R $ be a regular local ring, and $ f $ a regular parameter of $ R $. Quillen asked
whether every projective ${R_f} $-module is free. We settle this question when $ R $ is a …

Let $ k $ be an algebraically closed field of characteristic zero, $ R $ an affine $ k $-algebra.
We prove that if the ideal of the variety of $ R $ can be generated by an $ S $-sequence of …

Let $ R^ p\subseteq R'\subseteq R $ be a tower of commutative rings where $ R $ is a
regular affine domain over an algebraically closed field of prime characteristic $ p $ and …

In this paper we prove a finiteness result for infinite minimal free resolutions over a
Noetherian local ring R: If M is a module, such as the residue field, that is locally free of …

S, R s SrI. We construct a resolution of k over R. 1996 Academic Press, Inc. wx In what
follows, k is a field and S s kx,..., x is the polynomial ring 1 n in n variables over k. The …

Let A be a noetherian Auslander regular ring and δ the canonical dimension function on A-
modules, which is defined as δ (M)= d− j (M) where d is the global dimension of A and j (M) …