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Local cohomology over homogeneous rings with one-dimensional local base ring. (English) Zbl 1041.13012

Let \(R\), the direct product of rings \(R_n\), \(n>0\) or \(n=0\), be a homogeneous Noetherian ring with local base ring \(R_0\), \(M\) a finitely generated graded \(R\)-module. The main result in this paper shows that certain quotients and submodules of the local cohomology module are Artinian, provided the base ring \(R_0\) is of dimension \(<1\) or \(=1\). Using the results above, the authors give some properties of a local cohomology modules. In addition, some examples related to previous results are presented.

MSC:

13D45 Local cohomology and commutative rings
13E10 Commutative Artinian rings and modules, finite-dimensional algebras
13A02 Graded rings
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