Algebras and Representation Theory

, Volume 9, Issue 2, pp 217–226

Independence of the Total Reflexivity Conditions for Modules



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 ExtRi(M,R)=0 for all i>0, but ExtRi(M*,R)≠0 for all i>0.


totally reflective 


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  1. 1.
    Auslander, M. and Bridger, M.: Stable Module Theory, Mem. Amer. Math. Soc. 94, Amer. Math. Soc., Providence, RI, 1969. Google Scholar
  2. 2.
    Avramov, L. L. and Buchweitz, R.-O.: Support varieties and cohomology over complete intersections, Invent. Math. 142 (2000), 285–318. MathSciNetCrossRefGoogle Scholar
  3. 3.
    Avramov, L. L., Buchweitz, R.-O. and Sally, J. D.: Laurent coefficients and Ext of finite graded modules, Math. Ann. 307 (1997), 401–415. MathSciNetCrossRefGoogle Scholar
  4. 4.
    Avramov, L. and Martsinkovsky, A.: Absolute, relative, and Tate cohomology of modules of finite Gorenstein dimension, Proc. London Math. Soc. 85 (2002), 393–440. MathSciNetCrossRefGoogle Scholar
  5. 5.
    Fröberg, R.: Koszul algebras, In: Advances in Commutative Ring Theory (Fez, 1997), Lecture Notes in Pure and Appl. Math. 205, Dekker, New York, 1999, pp. 337–350. Google Scholar
  6. 6.
    Gasharov, V. and Peeva, I.: Boundedness versus periodicity over commutative local rings, Trans. Amer. Math. Soc. 320 (1990), 569–580. MathSciNetCrossRefGoogle Scholar
  7. 7.
    Jorgensen, D. A. and Şega, L. M.: Nonvanishing cohomology and classes of Gorenstein rings, Adv. Math. 188 (2004), 470–490. MathSciNetCrossRefGoogle Scholar
  8. 8.
    Lescot, J.: Asymptotic properties of Betti numbers of modules over certain rings, J. Pure Appl. Algebra 38 (1985), 287–298. MATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    Yoshino, Y.: A functorial approach to modules of G-dimension zero, Illinois J. Math. 49 (2005), 345–367. MATHMathSciNetGoogle Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Texas at ArlingtonArlingtonU.S.A.
  2. 2.Department of MathematicsMichigan State UniversityEast LansingU.S.A.

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