This paper deals with computing the global dimension of endomorphism rings of maximal
Cohen–Macaulay (= MCM) modules over commutative rings. Several examples are …

We show that for a finitely generated module M over a complete intersection R, the
vanishing of for a certain number of consecutive values of i starting at n forces the projective …

For a Noetherian ring R and a cotilting R-module T of injective dimension at least 1, we
prove that the derived dimension of R with respect to the category XT is precisely the …

In this note, we introduce a homological invariant for finitely generated modules over
commutative noetherian local rings by slightly modifying the definition of complete …

We introduce and investigate the notion of envelope dimension of commutative rings and
modules over them. In particular, we show that the envelope dimension of a ring,. We also …

Let R be a ring and let simp-R be a representative set of all simple (right R-) modules.
Denote by P< ω the class of all modules which are finitely generated and have finite …

This article is a report of three lectures given on “Dimension Theory of Noetherian Rings”, at
the meeting “Infinite Length Modules”, held in Bielefeld, from 7th to 11th September 1998. I …

We show that, if T is a selfsmall and selforthogonal module over a noetherian ring R of finite
global dimension with the endomorphism ring A, then fdTA⩽ gdA⩽ idRT+ fdTA. Applying the …

It is shown that, given any left artinian ring Λ which has vanishing radical cube and n
isomorphism classes of simple left modules, the global dimension of Λ is either infinite or …

The left global dimension of a semiprime ring, with left Krull dimension α≥ 1 is found to be
the supremum of the projective dimensions of the p-critical cyclic modules where β≤ α. A …