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IPM
30
YEARS OLD

“School of Mathematics”

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Paper   IPM / M / 8613
School of Mathematics
  Title:   Artinian local cohomology modules
  Author(s):  S. Yassemi (Joint with K. Borna Lorestani and P. Sahandi)
  Status:   Published
  Journal: Canad. Math. Bull.
  Vol.:  50
  Year:  2007
  Pages:   598-602
  Supported by:  IPM
  Abstract:
Let R be a commutative Noetherian ring, a an ideal of R and M a finitely generated R-module. Let t be a non-negative integer. It is known that if the local cohomology module Hi\fraka(M) is finitely generated for all i < t, then HomR(R/\fraka, Hi\fraka(M)) is finitely generated. In this paper it is shown that if Hi\fraka(M) is Artinian for all i < t, then HomR(R/\fraka, Hi\fraka(M)) need not be Artinian, but it has a finitely generated submodule N such that HomR(R/\fraka, Hi\fraka(M)) is Artinian.

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