Finiteness aspects of Gorenstein homological dimensions

Samir Bouchiba

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A short survey on Gorenstein global dimension

Driss Bennis (2010)

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This text gives a short overview of the recent works on Gorenstein global dimension of rings.

On Gorenstein Rings.

Overtoun M.G. Jenda (1988)

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Global Dimension of Differential Operator Rings. IV - Simple Modules.

Kenneth R. Goodearl (1989)

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Restricted homological dimensions over local homomorphisms and Cohen-Macaulayness

Fangdi Kong, Dejun Wu (2018)

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We define and study restricted projective, injective and flat dimensions over local homomorphisms. Some known results are generalized. As applications, we show that (almost) Cohen-Macaulay rings can be characterized by restricted homological dimensions over local homomorphisms.

A note on generalized Gorenstein dimension.

Wei, Jiaqun (2007)

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Tangent cones at Gorenstein singularities

Judith D. Sally (1980)

Compositio Mathematica

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Existence of Gorenstein projective resolutions and Tate cohomology

Peter Jørgensen (2007)

Journal of the European Mathematical Society

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Existence of proper Gorenstein projective resolutions and Tate cohomology is proved over rings with a dualizing complex. The proofs are based on Bousfield Localization which is originally a method from algebraic topology.

On the Gorenstein property of form rings.

M. Herrmann, J. Ribbe, P. Schenzel (1993)

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A noncommutative generalization of Auslander's last theorem.

Enochs, Edgar E., Jenda, Overtoun M.G., López-Ramos, J.A. (2005)

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Gorenstein property and symmetry for one dimensional local Cohen-Macaulay rings.

K. Kiyek, A. Compillo, F. Delgado (1994)

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Minimal injective resolutions with applications to dualizing modules and Gorenstein modules

Robert Fossum, Hans-Bjorn Foxby, Phillip Griffith, Idun Reiten (1975)

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