Some Results on Local Cohomology Modules
نویسنده
چکیده
Let R be a commutative Noetherian ring, a an ideal of R, and let M be a finitely generated R-module. For a non-negative integer t, we prove that H a(M) is a-cofinite whenever H t a(M) is Artinian and H i a(M) is a-cofinite for all i < t. This result, in particular, characterizes the a-cofiniteness property of local cohomology modules of certain regular local rings. Also, we show that for a local ring (R, m), f − depth(a, M) is the least integer i such that H a(M) ≇ H m(M). This result in conjunction with the first one, yields some interesting consequences. Finally, we extend the nonvanishing Grothendieck’s Theorem to a-cofinite modules.
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