본문 바로가기
KERD
논문KCI 등재

Some finiteness results for co-associated primes of generalized local homology modules and applications

1

조회

0

다운로드

1

인용

0

참고문헌

키워드

주제분류수학

초록

We prove some results about the finiteness of co-associated primes of generalized local homology modules inspired by a conjecture of Grothendieck and a question of Huneke. We also show some equivalent properties of minimax local homology modules. By duality, we get some properties of Herzog's generalized local cohomology modules.

Abstract

We prove some results about the finiteness of co-associated primes of generalized local homology modules inspired by a conjecture of Grothendieck and a question of Huneke. We also show some equivalent properties of minimax local homology modules. By duality, we get some properties of Herzog's generalized local cohomology modules.

참고문헌 (30)

  1. M. Aghapournahr, "Finiteness properties of minimax and coatomic local cohomology modules", Arch. Math. (Basel), 94(6), pp.519~528 (2010)[DOI]
  2. K. Bahmanpour, "On the coniteness of local cohomology modules", Proc. Amer. Math. Soc, 136(7), pp.2359~2363 (2008)[DOI]
  3. M. P. Brodmann, "A niteness result for associated primes of local cohomology modules", Proc. Amer. Math. Soc, 128(10), pp.2851~2853 (2000)[DOI]
  4. M. P. Brodmann, "Cambridge Studies in Advanced Mathematics", pp.60~ (1998), Cambridge University Press
  5. N. T. Cuong, "The I-adic completion and local homology for Artinian modules", Math. Proc. Cambridge Philos. Soc, 131(1), pp.61~72 (2001)[DOI]
  6. N. T. Cuong, "A local homology theory for linearly compact modules", J. Algebra, 319(11), pp.4712~4737 (2008)[DOI]
  7. K. Divaani-Aazar, "Associated primes of local cohomology modules", Proc. Amer. Math. Soc, 133(3), pp.655~660 (2005)[DOI]
  8. M. R. Doustimehr, "Faltings' local-global principle for the minimaxness of local cohomology modules", Comm. Algebra, 43(2), pp.400~411 (2015)[DOI]
  9. G. Faltings, "Der Endlichkeitssatz in der lokalen Kohomologie", Math. Ann, 255(1), pp.45~56 (1981)[DOI]
  10. A. Grothendieck, "Cohomologie locale des faisceaux coherents et theoremes de Lefschetz locaux et globaux (SGA 2)" (1968), North-Holland Publishing Co.
  11. R. Hartshorne, "Local cohomology", Lecture Notes in Mathematics, (41) (1967), Springer-Verlag
  12. R. Hartshorne, "Ane duality and coniteness", Invent. Math, 9, pp.145~164 (1970)[DOI]
  13. J. Herzog, "Komplexe, Auosungen und dualitat in der localen Algebra", pp.1970
  14. C. Huneke, "Problems on local cohomology, in Free resolutions in commutative algebra and algebraic geometry", Res. Notes Math., 2, pp.93~108 (1992)
  15. C. U. Jensen, "Les foncteurs derives de lim et leurs applications en theorie des modules", Lecture Notes in Mathematics, 254 (1972), Springer-Verlag
  16. M. Katzman, "An example of an innite set of associated primes of a local cohomology module", J. Algebra, 252(1), pp.161~166 (2002)[DOI]
  17. I. G. Macdonald, "Duality over complete local rings", Topology, 1, pp.213~235 (1962)[DOI]
  18. T. T. Nam, "Co-support and coartinian modules", Algebra Colloq, 15(1), pp.83~96 (2008)[DOI]
  19. T. T. Nam, "On the niteness of co-associated primes of local homology modules", J. Math. Kyoto Univ, 48(3), pp.521~527 (2008)[DOI]
  20. T. T. Nam, "A niteness result for co-associated and associated primes of generalized local homology and cohomology modules", Comm. Algebra, 37(5), pp.1748~1757 (2009)[DOI]
  21. T. T. Nam, "Left-derived functors of the generalized I-adic completion and generalized local homology", Comm. Algebra, 38(2), pp.440~453 (2010)
  22. T. T. Nam, "Generalized local homology for Artinian modules", Algebra Colloq., 19(1), pp.1205~1212 (2012)
  23. T. T. Nam, "Minimax modules, local homology and local cohomology", Internat. J. Math, 26(12), pp.16~ (2015)[DOI]
  24. T. T. Nam, "The niteness of coassociated primes of generalized local homology modules", Math. Notes, 97(5-6), pp.738~744 (2015)[DOI]
  25. A. K. Singh, "p-torsion elements in local cohomology modules", Math. Res. Lett., 7(2-3), pp.165~176 (2000)[DOI]
  26. N. Suzuki, "On the generalized local cohomology and its duality", J. Math. Kyoto Univ, 18(1), pp.71~85 (1978)
  27. S. Yassemi, "Coassociated primes", Comm. Algebra, 23(4), pp.1473~1498 (1995)[DOI]
  28. D. N. Yen, "Generalized local homology and duality", Internat. J. Algebra Comput, 29(3), pp.581~601 (2019)
  29. H. Zoschinger, "Linear-kompakte Moduln uber noetherschen Ringen", Arch. Math. (Basel), 41(2), pp.121~130 (1983)
  30. H. Zoschinger, "Minimax-moduln", J. Algebra, 102(1), pp.1~32 (1986)

관련 논문AI추천

이 간행물의 다른 논문 (10건)