Title of article :
Associated primes of local cohomology modules and Matlis duality
Author/Authors :
Kamal Bahmanpour، نويسنده , , Reza Naghipour، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2008
Pages :
10
From page :
2632
To page :
2641
Abstract :
Let be a commutative Noetherian local ring of dimension d and I an ideal of R. We show that the set of associated primes of the local cohomology module is finite whenever R is regular. Also, it is shown that if x1,…,xd is a system of parameters for R, then has infinitely many associated prime ideals for all i d−1, where D(−):=HomR(−,E) denotes the Matlis dual functor and is the injective hull of the residue field . Finally, we explore a counterexample of Grothendieckʹs conjecture by showing that, if d 3, then the R-module is not finitely generated, where I=(x1)∩(x2,…,xd).
Keywords :
local cohomology , Matlis duality , regular local ring , Associated primes , Cofinite module , Cohomological dimension
Journal title :
Journal of Algebra
Serial Year :
2008
Journal title :
Journal of Algebra
Record number :
698788
Link To Document :
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