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| Paper IPM / M / 9493 |
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| Abstract: | |
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Let M be a finite module over a commutative noetherian ring R. For ideals \fa and \fb of R, the relations between cohomological dimensions of M with respect to \fa, \fb, \fa∩\fb and \fa+ \fb are studied. When R is local, it is shown that M is generalized Cohen-Macaulay if there exists an ideal \fa such that all local cohomology modules of M with respect to \fa have finite lengths. Also, when r is an integer such that 0 ≤ r < dimR(M), any maximal element \fq of the non-empty set of ideals {\fa : \"\fai(M) is not artinian for some i, i ≥ r} is a prime ideal and that all Bass numbers of \"\fqi(M) are finite for all i ≥ r.
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