If R is a polynomial ring over a field k, M is a finitely generated graded R-module (for the
standard grading of R) and m:= R> 0, the invariants ai (M):= inf {µ| Hi m (M)> µ= 0} and bi …

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 …

Regularity of the powers of an ideal Page 1 COMMUNICATIONS IN ALGEBRA, 25(12), 3773-3776
(1997) REGULARITY OF THE POWERS OF AN IDEAL KAREN A. CHANDLER DEPARTMENT …

We establish bounds for the Castelnuovo–Mumford regularity of a finitely generated graded
module and its symmetric powers in terms of the degrees of the generators of the module …

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}} …

The Castelnuovo-Mumford regularity reg (I) is one of the most important invariants of a
homogeneous ideal I in a polynomial ring. A basic question is how the regularity behaves …

Regularity....................................................... 1 1.2 A Lemma from Homological Algebra and the
Equivalenceof the Definitions................................................ 3 1.3 Other Definitions and Further …

We extend the regularity criterion of Bayer-Stillman for a graded ideal $\mathfrak {a} $ of a
polynomial ring $ K [\underline {\bf x}]:= K [\underline {\bf x} _0,\dots,{\bf x} _r] $ over an …

This note has two goals. The first is to give a short and self contained introduction to the
Castelnuovo–Mumford regularity for standard graded rings R=⊕ i∈ ℕ R i over general base …

Let R be a standard graded ring over a commutative Noetherian ring with unity. Let I be an
arbitrary graded ideal of R and M an arbitrary finitely generated graded R-module. We prove …