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Paper   IPM / M / 7295
School of Mathematics
  Title:   Gorenstein test modules
1.  J. Asadollahi
2.  Sh. Salarian
  Status:   Published
  Journal: Comm. Algebra
  Vol.:  33
  Year:  2005
  Pages:   3439 – 3446
  Supported by:  IPM
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 ji, 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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