Integral closure has played a role in number theory and algebraic geometry since the
nineteenth century, but a modern formulation of the concept for ideals perhaps began with …

Integral Closure gives an account of theoretical and algorithmic developments on the
integral closure of algebraic structures. These are shared concerns in commutative algebra …

0. Introduction. Let R he a Noetherian ring and I be a regular ideal in R.(By ring we mean a
commutative ring with unity, and by a regular ideal we mean one that contains a …

The growth of Hilbert coefficients for powers of ideals are studied. For a graded ideal I in the
polynomial ring S= K [x1,..., xn] and a finitely generated graded S-module M, the Hilbert …

Abstract The Ratliff-Rush ideal associated to a nonzero ideal I in a commutative Noetherian
domain R with unity is Ĩ=⋃∞ n= 1 (I n+ 1: RI n=⋂{IS∩ R: S∈ B (I)}, where B (I)={R [I/a] P: a∈ …

Let (R, m) be a local Cohen–Macaulay ring and let I be an m-primary ideal. In this paper we
give sharp bounds on the multiplicity of the special fiber ring F of I in terms of other well …

The core of an ideal is the intersection of all its reductions. We describe the core of a zero-
dimensional monomial ideal I as the largest monomial ideal contained in a general …

Derivations and rational powers of ideals | SpringerLink Skip to main content Advertisement
SpringerLink Log in Menu Find a journal Publish with us Search Cart 1.Home 2.Archiv der …

Let (A, m, k) be a d-dimensional (d≥ 1) quasi-unmixed analytically unramified local domain
with infinite residue field. If I is an m-primary ideal, Shah defined the first coefficient ideal of I …

We exhibit an example of a product of two proper monomial ideals such that the residue
class ring is not Golod. We also discuss the strongly Golod property for rational powers of …