On connectedness and indecomposibility of local cohomology modules
Tóm tắt
Let I denote an ideal of a local Gorenstein ring
$${(R, \mathfrak m)}$$
. Then we show that the local cohomology module
$${H^c_I(R)}$$
, c = height I, is indecomposable if and only if V(I
d
) is connected in codimension one. Here I
d
denotes the intersection of the highest dimensional primary components of I. This is a partial extension of a result shown by Hochster and Huneke in the case I the maximal ideal. Moreover there is an analysis of connectedness properties in relation to various aspects of local cohomology. Among others we show that the endomorphism ring of
$${H^c_I(R)}$$
is a local Noetherian ring if dim R/I = 1.
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