Let $(R,\mathfrak m) $ be a Cohen-Macaulay local ring of dimension $ d\geq 2$ and $ I $ an
$\mathfrak m $-primary ideal. Let rd $(I) $ be the reduction number of $ I $ and n $(I) $ the …

This paper studies questions connected with when the Rees algebra of an ideal or the
formring of an ideal is Gorenstein. The main results are for ideals of small analytic deviation …

Let (A, m) be a Noetherian local ring, let M be a finitely generated Cohen–Macaulay A-
module of dimension r≥ 2 and let I be an ideal of definition for M. Set LI (M)=⨁ n≥ 0 M/I n+ …

Let $ S $ be a polynomial ring over a field. For a graded $ S $-module generated in degree
at most $ P $, the Castelnuovo-Mumford regularity of each of (i) its $ n^{\operatorname {th}} …

Let I be a homogeneous ideal of the polynomial ring K [x0,…, xn], where K is an arbitrary
field. Avoiding the construction of a minimal graded free resolution of I, we provide effective …

Let (R, m) be a Cohen-Macaulay local ring of dimension d≥ 3 and I an integrally closed m-
primary ideal. We establish bounds for the third Hilbert coefficient e 3 (I) in terms of the lower …

Let $(R,\mathfrak {m}) $ be a Noetherian local ring such that $\widehat {R} $ is reduced. We
prove that, when $\widehat {R} $ is $ S_2 $, if there exists a parameter ideal $ Q\subseteq R …

LetAbe a Cohen–Macaulay local ring with an infinite residue field and letI⊂ Abe an ideal of
heighth> 0. Supposing that depthA/Inis high enough for certain values ofn, we give in this …

This note provides first a generalization of the stabilization result of Eisenbud and Ulrich for
the regularity of powers of an $\mathfrak {m} $-primary ideal to the case of ideals that are not …

Our main theorem shows that the regularity of nondegenerate homogeneous prime ideals is
not bounded by any polynomial function of the degree; this holds over any field $ k $. In …