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The membership of the local cohomology modules Han(M) of a module M in certain Serre subcategories of the category of modules is studied from below (i<n) and from above (i>n). Generalizations of depth and regular sequences are defined. The relation of these notions to local cohomology are found. It is shown that the membership of the local cohomology modules of a finite module in a Serre subcategory...
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