“School of Mathematics”
Back to Papers HomeBack to Papers of School of Mathematics
| Paper IPM / M / 8718 |
|
| Abstract: | |
|
Let R = ⊕n ∈ \mathbbN0Rn be a Noetherian
homogeneous ring with local base ring (R0, \frakm0) and
irre1evant ideal R+, let M be a finitely generated graded
R-module. In this paper we show that
H1\frakm0R(H1R+(M)) is Artinian and
Hi\frakm0R(H1R+(M)) is Artinian for each i in
the case where R+ is principal. Moreover, for the case where
ara(R+) = 2, we prove that, for each i ∈ \mathbbN0,
Hi\frakm0R(H1R+(M)) is Artinian if and only if
Hi+2\frakm0R(H1R+(M)) is Artinian. We also prove
that Hd\frakm0R(HcR+(M)) is Artinian, where d = dim(R0) and c is the cohomological dimension of M with
respect to R+. Finally we present some examples which show that
H2\frakm0R(H1R+(M)) and H3\frakm0R(H1R+(M)) need not be Artinian.
Download TeX format |
|
| back to top | |
