In the last two decades Cohen-Macaulay rings and modules have been central topics in
commutative algebra. This book meets the need for a thorough, self-contained introduction …

Commutative Algebra is best understood with knowledge of the geometric ideas that have
played a great role in its formation, in short, with a view towards algebraic geometry. The …

In this paper we study vector spaces of matrices, all of whose elements have rank at most a
given number. The problem of classifying such spaces is roughly equivalent to the problem …

This book is a comprehensive treatment of the representation theory of maximal Cohen-
Macaulay (MCM) modules over local rings. This topic is at the intersection of commutative …

In the last few years the maximal Cohen-Macaulay modules over local rings of singularities
have been studied by methods of representation theory, commutative algebra, and algebraic …

This book provides an introduction to recent developments in the theory of blow up algebras-
Rees algebras, associated graded rings, Hilbert functions, and birational morphisms. The …

0.1. H. Kn/Srrer [Kn6] showed the following property of the local ring R of an isolated simple
hypersurface singularity: There are only finitely many isomorphism classes of …

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

This book presents an account of several conjectures arising in commutative algebra from
the pioneering work of Serre and Auslander-Buchsbaum. The approach is via Hochster's' …

This paper contributes to the liaison and obstruction theory of subschemes in $\mathbb {P}^
n $ having codimension at least three. The first part establishes several basic results on …