Algebras and Representation Theory

, Volume 9, Issue 2, pp 217-226

First online:

Independence of the Total Reflexivity Conditions for Modules

  • David A. JorgensenAffiliated withDepartment of Mathematics, University of Texas at Arlington Email author 
  • , Liana M. ŞegaAffiliated withDepartment of Mathematics, Michigan State University

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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.


totally reflective