Minimal Pure Injective Resolutions of Complete Rings.
The first term in a minimal pure injective resolution.
Gorenstein injective and projective modules.
Some remarks on global dimensions for cotorsion pairs
Abelian groups which have trivial absolute coGalois group
In this article we characterize those abelian groups for which the coGalois group (associated to a torsion free cover) is equal to the identity.
and -dimensions of modules
Kaplansky classes
The existence of envelopes
Copure injective resolutions, flat resolvents and dimensions
In this paper, we show the existence of copure injective preenvelopes over noetherian rings and copure flat preenvelopes over commutative artinian rings. We use this to characterize -Gorenstein rings. As a consequence, if the full subcategory of strongly copure injective (respectively flat) modules over a left and right noetherian ring has cokernels (respectively kernels), then is -Gorenstein.
On Cohen-Macaulay rings
In this paper, we use a characterization of -modules such that to characterize Cohen-Macaulay rings in terms of various dimensions. This is done by setting to be the local cohomology functor of with respect to the maximal ideal where is the Krull dimension of .
Binomial coefficients.
Remarks on commutative noetherian rings whose flat modules have flat injective envelopes
Trivial formal fibres and formal Laurent series
A noncommutative generalization of Auslander's last theorem.
On Matlis dualizing modules.
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