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Local Cohomology, Second Edition by R. Y. Sharp, M. P. Brodmann

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9

The Annihilator and Finiteness Theorems

There have been several examples earlier in this book of non-finitely generated local cohomology modules of finitely generated modules: for example, in 6.1.7, and also in 7.3.3, we saw that, if (R, images) is local, and N is a nonzero, finitely generated R-module of dimension n > 0, then images(N) is not finitely generated. Since images(N), being isomorphic to a submodule of N, is certainly finitely generated, it becomes of ...

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