“School of Mathematics”Back to Papers Home
Back to Papers of School of Mathematics
|Paper IPM / M / 7295||
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.
Download TeX format
|back to top|