“School of Mathematics”
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Paper IPM / M / 7295  


Abstract:  
Let (R,m) be a commutative Noetherian local ring. We exhibit
certain modules T over R which test Gdimension of a finitely
generated Rmodule M with finite Gdimension in the following
sense: if Ext^{j}_{G}(M,T)=0 for all j ≥ i, where
i is a positive integer, then Gdim_{R}M < i. Modules with the
property like T will be called Gorenstein test modules (Gtest
modules for short). It is known that R itself is a Gtest
module. We show that k, the residue field of R, also tests
Gdimension. Some more examples of Gtest 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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