Consider a Cohen-Macaulay local ring $(R,\mathfrak m) $ with dimension $ d\geq 2$, and
let $ I\subseteq R $ be an $\mathfrak m $-primary ideal. Denote $ r_ {J}(I) $ as the reduction …

Let A be a noetherian local ring of dimension d≥ 1 and depth (A)≥ d− 1. In this paper, we
study the non-positivity for the Hilbert coefficients of parameter ideals in the ring A …

Suppose G is a standard graded ring over an infinite field. We obtain a sharp lower bound
for the regularity of G in terms of the postulation number, the depth, and the dimension of G …

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 …

We establish a bound for the Castelnuovo–Mumford regularity of the associated graded ring
GI (A) of an m-primary ideal I of a local Noetherian ring (A, m) in terms of the dimension of A …

We extend the" linearly exponential" bound for the Castelnuovo-Mumford regularity of a
graded ideal in a polynomial ring 𝐾 [𝓍₁,..., 𝓍𝑟] over a field (established by Galligo and …

In this article, we consider ideals of the form I=∩ 1≤ i< j≤ n P i, jwi, j of a polynomial ring R=
K [x 1,…, xn] over a field, where P i, j is an ideal generated by variables {x 1,…, xn}∖{xi, xj} …

We establish a uniform bound for the Castelnuovo–Mumford regularity of associated graded
rings of parameter ideals in a generalized Cohen–Macaulay ring. As consequences, we …

We estimate the Castelnuovo-Mumford regularity of ideals in a polynomial ring over a field
by studying the regularity of certain modules generated in degree zero and with linear …

Let (A,[mfr]) be a local ring. For convenience we will assume throughout this paper that the
residue field of A is infinite. Let I be an ideal of A. An ideal J⊆ I is called a reduction of I if …