A FINITENESS RESULT FOR ATTACHED PRIMES OF ARTINIAN LOCAL COHOMOLOGY MODULES

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  • LE THANH NHAN
    College of Sciences, Thai Nguyen University, Thai Nguyen, Vietnam
  • NGUYEN VAN HOANG
    College of Education, Thai Nguyen University, Thai Nguyen, Vietnam

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<jats:p> Let (R, 𝔪) be a Noetherian local ring. For an integer s ≥ -1 and an Artinian R-module A, we introduce the notion of A-cosequence in dimension > s and show that the set of all attached primes [Formula: see text] satisfying dim (R/𝔭) ≥ s is a finite set whenever (x<jats:sub>1</jats:sub>, …, x<jats:sub>k</jats:sub>) is an A-cosequence in dimension > s. As an application, we give a finiteness result for attached primes of certain Artinian local cohomology modules of a finitely generated R-module. </jats:p>

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