Gorenstein injective dimension, Bass formula and Gorenstein rings

Details Gorenstein injective dimension, Bass formula and Gorenstein rings Gorenstein injective dimension, Bass formula and Gorenstein rings

2003-12-31

arxiv.org/abs/math/0312513v2

Mathematics

Commutative Algebra

13 pages, Main theorem in section 3 generalized, with new corollaries

Scientific paper

Let $(R,\frak m, k)$ be a noetherian local ring. It is well-known that $R$ is regular if and only if the injective dimension of $k$ is finite. In this paper it is shown that $R$ is Gorenstein if and only if the Gorenstein injective dimension of $k$ is finite. On the other hand a generalized version of the so-called Bass formula is proved for finitely generated modules of finite Gorenstein injective dimension. It also improves Christensen's generalized Bass formula (cf. "Gorenstein dimensions", volume 1747 of Lecture Notes in Mathematics, Springer-Verlag, Berlin, 2000).

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