Symmetry in vanishing of Tate cohomology over Gorenstein rings
classification
🧮 math.AC
keywords
gorensteincohomologyfinitelygeneratedlocalmathbbringssymmetry
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We investigate symmetry in the vanishing of Tate cohomology for finitely generated modules over local Gorenstein rings. For finitely generated R-modules M and N over Gorenstein local ring R, it is shown that $\widehat{Ext}^i_R(M,N)=0$ for all $i\in\mathbb{Z}$ if and only if $\widehat{Ext}^i_R(N,M)=0$ for all $i\in\mathbb{Z}$.
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