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Old 06-30-2012, 11:02 AM
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Artinianness of generalized local cohomology modules of, zd-modules

Ngo Thi Ngoan (Faculty of natural and social sciences - Thai Nguyen University), Nguyen Van Hoang (College of education - Thai Nguyen University), 1. Introduction, Throughout this paper, R is a commutative Noetherian ring with identity. Let I be an ideal, of R, and M, K be R-modules. For each integer i ≥ 0, the i-th generalized local cohomology, module of M and K is defined by J. Herzog in [5] as follows, (, ) lim ( /, ), i i n, IR, n, H M K Ext M I M K , ., It is clear that, ), ( K R Hi, I, =, ) (K Hi, I, . It is known that the generalized local cohomology, of finitely generated modules have many interesting properties. In particular, if (R, m) is a local, ring and M, K finitely generated R-modules, then the generalized local cohomology modules, ), ( K M Hi, m, are Artinian. Also, in the same situation, it is known that for d = dim R, the d-th, generalized local cohomology module of M and K with respect to any ideal I is Artinian. It will, be a noticeable achievement, if we could extend these results to generalized local cohomology of, a larger class of modules.

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local cohomology, phimsx zd

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