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| Paper IPM / M / 7295 |
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| Abstract: | |||||
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Let (R,m) be a commutative Noetherian local ring. We exhibit
certain modules T over R which test G-dimension of a finitely
generated R-module M with finite G-dimension in the following
sense: if ExtjG(M,T)=0 for all j ≥ i, where
i is a positive integer, then G-dimRM < i. Modules with the
property like T will be called Gorenstein test modules (G-test
modules for short). It is known that R itself is a G-test
module. We show that k, the residue field of R, also tests
G-dimension. Some more examples of G-test modules are introduced.
Finally we show that a dual statement is also true: k tests
Gorenstein injective dimension, using appropriate cohomology.
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