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Gorenstein derived functors
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Over any associative ring
R
R
it is standard to derive
H
o
m
R
(
−
,
−
)
\mathrm {Hom}_R(-,-)
using projective resolutions in the first variable, or injective resolutions in the second variable, and doing this, one obtains
E
x
t
R
n
(
−
,
−
)
\mathrm {Ext}_R^n(-,-)
in both cases. We examine the situation where projective and injective modules are replaced by Gorenstein projective and Gorenstein injective ones, respectively. Furthermore, we derive the tensor product
−
⊗
R
−
-\otimes _R-
using Gorenstein flat modules.
American Mathematical Society (AMS)
Title: Gorenstein derived functors
Description:
Over any associative ring
R
R
it is standard to derive
H
o
m
R
(
−
,
−
)
\mathrm {Hom}_R(-,-)
using projective resolutions in the first variable, or injective resolutions in the second variable, and doing this, one obtains
E
x
t
R
n
(
−
,
−
)
\mathrm {Ext}_R^n(-,-)
in both cases.
We examine the situation where projective and injective modules are replaced by Gorenstein projective and Gorenstein injective ones, respectively.
Furthermore, we derive the tensor product
−
⊗
R
−
-\otimes _R-
using Gorenstein flat modules.
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