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

Hilbert Functions play major roles in Algebraic Geometry and Commutative Algebra, and are
becoming increasingly important also in Computational Algebra. They capture many useful …

In this paper we introduce a new technique to study associated graded modules. Let (A, m)
be a Noetherian local ring with depthA≥ 2. Our techniques give a necessary and sufficient …

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 Cohen-Macaulay local ring of dimension $ d\geq 3$ and $ I $
an $\mathfrak {m} $-primary ideal of $ R $. Let $ r_J (I) $ be the reduction number of $ I …

Let be an excellent two-dimensional normal local domain. In this paper, we study the elliptic
and the strongly elliptic ideals of A with the aim to characterize elliptic and strongly elliptic …

Hilbert functions of Cohen–Macaulay local rings Page 190 Contemporary Mathematics Volume
555 , 2011 Hilbert Functions of Cohen-Macaulay local rings Maria Evelina Rossi Abstract. This …

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+ …

We prove new results on the interplay between reduction numbers and the Castelnuovo–
Mumford regularity of blowup algebras and blowup modules, the key basic tool being the …

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 …