COHEN-MACAULAY DIMENSION OF MODULES OVER NOETHERIAN RINGS Page 1 ROCKY
MOUNTAIN JOURNAL OF MATHEMATICS Volume 35, Number 4, 2005 COHEN-MACAULAY …

Let R be a commutative ring with identity. Call an R-module almost Artinian if every proper
homomorphic image is Artinian. If A is an almost Artinian R-module that is not Artinian, then …

Let R be an associative ring and denote by the injective hull of the right module RR. If can be
endowed with a ring multiplication which extends the existing module multiplication, we say …

If R is a commutative Noetherian ring of Krull dimension n, then it follows from a celebrated
theorem of Serre [1, Theorem IV. 2.5] that all finitely generated indecomposable projective …

It has been known for some time that if a ring R has a faithful monoform module p, M then R
can be embedded in a ring of linear transformations End VA over a division ring A (where V …

Serre's theorem on projective modules says roughly that if a projective R module is big
enough it can map onto R. Forster and Swan discuss how big a free module is needed to …

For commutative rings we don't have to assume any sort of chain conditions on the ring A/N.
Before stating and proving the commutative result we recall a few results concerning the …

Let A be a Cohen-Macaulay local ring, and let C'(A) be the class of all finitely generated A-
modules which are of finite projective dimension and of codimension at least r. The …

Throughout this note, A will denote a commutative Noetherian integral domain (with non-
zero identity) for which 0< dim A< oo (so that A is not a field). Here, dim A denotes the …