Finiteness of graded local cohomology modules |
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Authors: | Reza Sazeedeh |
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Institution: | Department of Mathematics, Urmia University, Urmia, Iran Institute for Studies in Theoretical Physics and Mathematics (IPM), Tehran, Iran |
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Abstract: | Let R=?n∈N0Rn be a Noetherian homogeneous ring with local base ring (R0,m0) and irrelevant ideal R+, let M be a finitely generated graded R-module. In this paper we show that is Artinian and is Artinian for each i in the case where R+ is principal. Moreover, for the case where , we prove that, for each i∈N0, is Artinian if and only if is Artinian. We also prove that is Artinian, where and c is the cohomological dimension of M with respect to R+. Finally we present some examples which show that and need not be Artinian. |
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Keywords: | Primary 13D45 13E10 |
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