… The purpose of these notes is to present a structure theory for Artinian modules over a 1-dimensional,
Noetherian, Cohen-Macaulay ring, and to show that many of the properties of such …

… under flat base extensions of the ground ring. As a basic reference of all of the unexplained
terminology we use H. Matsumura’s textbook [M]. For the results about CohenMacaulay rings …

… theorems for CohenMacaulay local rings of finite CM type in dimensions zero and one. …
-dimensional rings via the conductor-square construction. The two-dimensional Cohen-Macaulay …

… ffat dimension is also a refinement of other dimension … ’ and Jenda’s Gorenstein flat dimension
GfdR introduced in [15]. … is a refinement of the Cohen–Macaulay dimension CM-dimR of …

… CM-dimension is infinite while GCM-dimension is finite. … Cohen– Macaulay, then this will
give an example of a module with infinite GCM-dimension and finite restricted flat dimension. …

… If e is in U, the lemma below shows that X is flat over U and any … dimension of the components
of G - W containing e, and set d = dim G - m. A regular subspace H of G, of dimension less …

… which becomes an equality when tjJ has finite flat dimension, and rp is flat or R is Cohen-Macaulay.
It is not known whether equality holds when both tjJ and rp have finite flat dimension, …

… dimensional local CohenMacaulay rings of embedding dimension e + d - 1 and for d-dimensional
local Gorenstein rings of embedding dimension e -+ d - 2. The main results will be …

… Recall that B is called a balanced big Cohen–Macaulay algebra for the local ring (R,m) if …
every local ring of dimension at most three has a balanced big Cohen–Macaulay algebra. In fact…

… ring over a field is CohenMacaulay, and a grade r ideal … flat, p is not a zero divisor on I, and
hence p is not a zero divisor on IZ [x] Q. Then Z[x] Q/IZ [x] Q is CohenMacaulay of dimension …