nLab Gorenstein ring



A Gorenstein ring, RR, is a commutative Noetherian local ring of finite injective dimension over itself. It follows then that its injective dimension is equal to rr = Krull dimension(R)(R), and that Ext R *(k,R)Ext^{\ast}_R(k, R) is one dimensional as a kk-vector space, where kk is the residue field of RR.


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