• Received : 2017.09.04
  • Accepted : 2018.04.25
  • Published : 2018.10.31


It is shown that any equidimensional local ring which has finite Cousin cohomology modules with respect to the dimension filtration has a uniform local cohomological annihilator and is universally catenary.


Supported by : Payame Noor University


  1. M. P. Brodmann and R. Y. Sharp, Local Cohomology: An Algebraic Introduction with Geometric Applications, Cambridge Studies in Advanced Mathematics, 60, Cambridge University Press, Cambridge, 1998.
  2. W. Bruns and J. Herzog, Cohen-Macaulay Rings, Cambridge Studies in Advanced Mathematics, 39, Cambridge University Press, Cambridge, 1993.
  3. M. T. Dibaei, A study of Cousin complexes through the dualizing complexes, Comm. Algebra 33 (2005), no. 1, 119-132.
  4. M. T. Dibaei and R. Jafari, Modules with finite Cousin cohomologies have uniform local cohomological annihilators, J. Algebra 319 (2008), no. 8, 3291-3300.
  5. M. T. Dibaei and M. Tousi, The structure of dualizing complex for a ring which is ($S_2$), J. Math. Kyoto Univ. 38 (1998), no. 3, 503-516.
  6. M. T. Dibaei and M. Tousi, A generalization of the dualizing complex structure and its applications, J. Pure Appl. Algebra 155 (2001), no. 1, 17-28.
  7. R. Hartshorne, Residues and Duality, Lecture notes of a seminar on the work of A. Grothendieck, given at Harvard 1963/64. With an appendix by P. Deligne. Lecture Notes in Mathematics, No. 20, Springer-Verlag, Berlin, 1966.
  8. T. Kawasaki, Finiteness of Cousin cohomologies, Trans. Amer. Math. Soc. 360 (2008), no. 5, 2709-2739.
  9. J. Lipman, S. Nayak, and P. Sastry, Pseudofunctorial behavior of Cousin complexes on formal schemes, in Variance and duality for Cousin complexes on formal schemes, 3-133, Contemp. Math., 375, Amer. Math. Soc., Providence, RI, 2005.
  10. J. J. Rotman, An Introduction to Homological Algebra, Pure and Applied Mathematics, 85, Academic Press, Inc., New York, 1979.
  11. R. Y. Sharp, The Cousin complex for a module over a commutative Noetherian ring, Math. Z. 112 (1969), 340-356.
  12. R. Y. Sharp, Gorenstein modules, Math. Z. 115 (1970), 117-139.
  13. R. Y. Sharp, A Cousin complex characterization of balanced big Cohen-Macaulay modules, Quart. J. Math. Oxford Ser. (2) 33 (1982), no. 132, 471-485.
  14. C. Zhou, Uniform annihilators of local cohomology, J. Algebra 305 (2006), no. 1, 585- 602.