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

Brodmann, M.; Fumasoli, S.; Tajarod, R.

Proc. Am. Math. Soc. 131, No. 10, 2977-2985 (2003).

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.

Reviewer: Tong Wenting (Nanjing)

MSC:

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

Keywords:

direct product of rings; Noetherian ring; graded module; Artinian local cohomology module