Remarks on a depth formula, a grade inequality and a conjecture of Auslander Page 1
COMMUNICATIONS IN ALGEBRA, 26(1 l), 3793-3806 (1998) Remarks on a depth formula, a …

All rings considered are commutative with identity and all ring extensions are unital. Let R be
a ring with total quotient ring T. The integral minimal ring extensions of R are catalogued via …

Let Q be a (Noetherian) local ring with maximal ideal m, and let p be a prime ideal in Q such
that dim p+ rank p= dim Q. Serre showed, using homological means, that if Q is regular, then …

Some theorems in [4] indicate that the injective modules over a ring R provide a great deal of
information about the structure of the ring. More recently, the papers of H. Bass [9] and C …

The notion of the reduced rank of a finitely generated module over a right Soetherian ring
was first intrnduced in [S] but has been little used until recently. Our aim in this paper is to …

In [l, p. 470] Professor Hyman Bass mentions the following conjecture: a ring P is left perfect
if, and only if, every nonzero left P-module has a maximal submodule and P has no infinite …

i < v > Page 1 THE AUSLANDER CONDITION ON GRADED AND NOETHERIAN RINGS Eva
Kristina Ekstrom Department of Mathematics University of Stockholm Box 670 1 11385 …

In the 1ate s. iHties H. Aus lander in tr" oduced var i oua homo I og iea I conditions on
noetherian, or more generally coherent rings which then were investigated both for …

One of the pervasive themes in the theory of Noetherian rings has been the study of
localization and (classical) quotient rings. This was started, of course, by Goldie's theorems …

Over-rings (rings between an integral domain and its quotient field) have long played a
prominent role in commutative algebra. Tn number theory the valuation rings lying over a …