, Volume 9, Issue 2, pp 217-226

Independence of the Total Reflexivity Conditions for Modules

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We show that the conditions defining total reflexivity for modules are independent. In particular, we construct a commutative Noetherian local ring R and a reflexive R-module M such that Ext R i (M,R)=0 for all i>0, but Ext R i (M *,R)≠0 for all i>0.