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 …

Let (R, m) be a Noetherian local ring of dimension d> 0, and let I be an mprimary ideal. One
of our goals is to study the set of I-good filtrations of R. More concretely, we will consider the …

We establish new classes of Ratliff-Rush closed ideals and some pathological behavior of
the Ratliff-Rush closure. In particular, Ratliff-Rush closure does not behave well under …

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 (R, m) be ad-dimensional Noetherian local ring, M be an R-submodule of the free
module F= R p. In this work, in analogy to the papers of Liu in and of Ratliff and Rush in, if …

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+ …

This paper gives new bounds on the first Hilbert coefficient of an ideal of finite colength in a
Cohen-Macaulay local ring. The bound given is quadratic in the multiplicity of the ideal. We …

Let (R, m) be a d-dimensional Cohen–Macaulay local ring. In this paper we prove, in a very
elementary way, an upper bound of the first normalized Hilbert coefficient of a m-primary …

Let R be a commutative Noetherian ring, M a finitely generated R-module and I a proper
ideal of R. In this paper we introduce and analyze some properties of r (I, M)=⋃ k⩾ 1 (Ik+ 1M …