 About 84,600 results  books.google.com The purpose of these notes is to explain in detail some topics on the intersection of commutative algebra, representation theory and singularity theory. 

 books.google.com This book meets the need for a thorough, selfcontained introduction to the homological and combinatorial aspects of the theory of CohenMacaulay rings, Gorenstein rings, local cohomology, and canonical modules. 

 books.google.com Y. Yoshino, Hideyuki Matsumura. Chapter 1. Preliminaries In this chapter we will
review some basic facts without proofs and give some of the basic notation that
will be used throughout the book. For further results in commutative algebra we ... 

 books.google.com This book is a comprehensive treatment of the representation theory of maximal CohenMacaulay (MCM) modules over local rings. 

 books.google.com The study of CohenMacaulay modules over Noetherian local rings originates
from the theory of integral representations of finite groups (which, on its side,
grew up from a very classical problem of classification of crystallographic groups,
... 

 books.google.com First, we recall that a module M of finite type over a local ring R is called a Cohen
Macaulay module if depth M = dim M. In general, depth M < dim M < dim R. If
depth M = dim M = dim R we call M a maximal CohenMacaulay module. If R
itself ... 

 books.google.com Definition 3.3.7 (Big CohenMacaulay Modules). Let R be a Noetherian local ring,
and let M be an arbitrary Rmodule. We call M a big CohenMacaulay module, if
there exists a system of parameters in R which is Mregular. If moreover every ... 

 books.google.com Definition of CohenMacaulay modules By prop. 7, for every pe Ass(E), we have
dim(A/p) > depth(E). Since dim E = sup dim(A/p) for p e Ass(E), we have in
particular dim E > depth E. Definition 1. The module E is called a Cohen
Macaulay ... 

 books.google.com nonzero finitely generated module M is CohenMacaulay if and only if M is
projective, or equivalently, if and only if M is torsion free; d) if R is a regular ring,
then a finitely generated 72module M is CohenMacaulay if and only if M is
projective; ... 

 books.google.com Michiel Hazewinkel  1994  Preview A regular local ring (and, in general, any Gorenstein ring) is a Cohen  Macaulay
ring; any Artinian ring, any one dimensional reduced ring ... A module M over a
local ring A is called a Cohen Macaulay module if its depth equals its dimension. 

 