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 …

Local cohomology is a useful tool in several branches of commutative algebra and algebraic
geometry. The main aim of this series of lectures is to illustrate a few of these techniques …

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

Since a projective variety V= Z (I)⊆ P n is an intersection of hypersurfaces, one of the most
basic problems we can pose in relation to V is to describe the hypersurfaces containing it. In …

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 …

Let $(A,\mathcal {M}) $ be a local ring of positive dimension $ d $ and let $ I $ be an
$\mathcal {M} $-primary ideal. We denote the reduction number of $ I $ by $ r (I) $, which is …

Depth of associated graded rings via Hilbert coefficients of ideals - ScienceDirect Skip to main
contentSkip to article Elsevier logo Journals & Books Search RegisterSign in View PDF …

The-multiplicity plays an important role in the intersection theory of Stückrad–Vogel cycles,
while recent developments confirm the connections between the-multiplicity and …

Hilbert Coefficients of Hilbert Filtrations Page 1 Ž . JOURNAL OF ALGEBRA 199, 4061 1998
ARTICLE NO. JA977194 Hilbert Coefficients of Hilbert Filtrations A. Guerrieri* Dip. di …