SYMMETRY IN THE VANISHING OF EXT OVER GORENSTEIN RINGS

We investigate symmetry in the vanishing of Ext for finitely generated modules over local Gorenstein rings. In particular, we define a class of local Gorenstein rings, which we call AB rings, and show that for finitely generated modules M and N over an AB ring R, $\mathrm{E}\mathrm{x}{\mathrm{t}}_{\...

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Bibliographic Details
Published in:Mathematica scandinavica 2003-12, Vol.93 (2), p.161-184
Main Authors: HUNEKE, CRAIG, JORGENSEN, DAVID A.
Format: Article
Language:English
Subjects:
Algebra
Mathematical rings
Tensors
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Summary:We investigate symmetry in the vanishing of Ext for finitely generated modules over local Gorenstein rings. In particular, we define a class of local Gorenstein rings, which we call AB rings, and show that for finitely generated modules M and N over an AB ring R, $\mathrm{E}\mathrm{x}{\mathrm{t}}_{\mathrm{R}}^{\mathrm{i}}(\mathrm{M},\mathrm{N})=0$ for all i » 0 if and only if $\mathrm{E}\mathrm{x}{\mathrm{t}}_{\mathrm{R}}^{\mathrm{i}}(\mathrm{N},\mathrm{M})=0$ for all i » 0.
ISSN:0025-5521
1903-1807
DOI:10.7146/math.scand.a-14418