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Paper   IPM / M / 8434
School of Mathematics
  Title:   On the finiteness properties of associated primes of generalized local cohomology modules
  Author(s):  K. Khashyarmanesh
  Status:   Published
  Journal: Forum Math.
  Vol.:  20
  Year:  2008
  Pages:   265–273
  Supported by:  IPM
Let R be a commutative Noetherian ring, \frak a an ideal of R and N an R-module. We prove that, for every finitely generated R-module of finite projective dimension t, the elements in the support of generalized local cohomology module Hn+t\frak a(M, N) of height n is finite for all n\geqslant 0. This implies that, if R is a d-dimensional local ring, then Hd+t−1\frak a(M, N) has finite support for arbitrary R, \frak a and N. In addition, for a non-negative integer n, we show that if M and N are arbitrary finitely generated R-modules such that the R-modules Hi\frak a( N) and Hi\frak a(M, N) have finite support for all i < n, then Ass Hn\frak a(M, N) is finite.

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