Independence of the total reflexivity conditions for modules

David Jorgensen; Liana Sega

Independence of the total reflexivity conditions for modules

Commutative Algebra 2007-05-23 v2

Authors: David Jorgensen , Liana Sega

Abstract

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 $\Ext^i_R(M,R)=0$ for all $i>0$ , but $\Ext^i_R(M^*,R)\ne 0$ for all $i>0$ .

Keywords

commutative algebra module theory

Cite

@article{arxiv.math/0410257,
  title  = {Independence of the total reflexivity conditions for modules},
  author = {David Jorgensen and Liana Sega},
  journal= {arXiv preprint arXiv:math/0410257},
  year   = {2007}
}

Comments

In the previous version, Proposition 2.1 is incorrect, as stated. We added the assumption "Artinian" in the statement

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