Gorenstein injective dimension, Bass formula and Gorenstein rings
نویسنده
چکیده
Let (R,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 the results by Enochs and Jenda [10] and Christensen [5].
منابع مشابه
A Bass formula for Gorenstein injective dimension
In this paper a generalized version of the Bass formula is proved for finitely generated modules of finite Gorenstein injective dimension over a commutative noetherian ring.
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