… Also, as an application, we show that any Cohen-Macaulay module that has a canonical
module with finite injective dimension satisfies the Auslander–Reiten conjecture. …

… ring. On the other hand, we discuss the homological dimensions of R in terms of P1-injective …
the following formula for the weak global dimension and the global dimension of a ring R: …

… Let T = ( A 0 U B ) be a formal triangular matrix ring, where A and B are rings and U is a ( B ,
… is a right coherent ring, U B has finite flat dimension, U A has finite flat or injective dimension, …

… for example all Gorenstein algebras and all representation-finite algebras. We prove that
the Gorenstein dimension of A coincides with the Gorenstein projective dimension of the …

… Section 7 deals with another related dimensions called the copure flat and the copure
injective dimension. Using the copure flat dimension we study n-Gorenstein skew group rings. …

… Throughout this paper we let R be a ring with identity, which is not necessarily … a Gorenstein
ring if it has finite injective dimension, as both a left and right module over itself. These rings …

… Gorenstein weak global dimension Gwgldim ( R ) of a ring R equals the supremum of the
Gorenstein flat dimensions … We also show that, if R is a coherent ring and x is a central nonzero-…

… all injective R-modules, we show the existence of a new left global Gorenstein dimension
of … -Chen rings by this new global Gorenstein dimension and show the existence of Ding-Chen …

… the Gorenstein-projective modules over a Morita ring … Gorenstein algebra and both MA and
AN (resp., both NB and BM) have finite projective dimension, then A (resp., B) is a Gorenstein …

… matrix ring is Gorenstein projective or Gorenstein injective under the “Gorenstein regular” …
Wang [3] investigated Gorenstein homological dimensions of modules over triangular matrix …