Cofiniteness and Artinianness of certain local cohomology modules
Let R be a commutative Noetherian ring, I , J be two ideals of R , M be an R -module and S be a Serre class of R -modules. A positive answer to the Huneke’s conjecture is given for a Noetherian ring R and minimax R -module M of Krull dimension less than 3, with respect to S . There are some results...
Gespeichert in:
Veröffentlicht in: | Ricerche di matematica 2016-06, Vol.65 (1), p.21-36 |
---|---|
Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Zusammenfassung: | Let
R
be a commutative Noetherian ring,
I
,
J
be two ideals of
R
,
M
be an
R
-module and
S
be a Serre class of
R
-modules. A positive answer to the Huneke’s conjecture is given for a Noetherian ring
R
and minimax
R
-module
M
of Krull dimension less than 3, with respect to
S
. There are some results on cofiniteness and Artinianness of local cohomology modules with respect to a pair of ideals. For a ZD-module
M
of finite Krull dimension and an integer
n
∈
N
, if
H
I
,
J
i
(
M
)
∈
S
for all
i
>
n
, then
H
I
,
J
i
(
M
)
/
a
j
H
I
,
J
i
(
M
)
∈
S
for any
a
∈
W
~
(
I
,
J
)
, all
i
≥
n
, and all
j
≥
0
. By introducing the concept of Serre cohomological dimension of
M
with respect to (
I
,
J
), for an integer
r
∈
N
0
,
H
I
,
J
j
(
R
)
∈
S
for all
j
>
r
iff
H
I
,
J
j
(
M
)
∈
S
for all
j
>
r
and any finite
R
-module
M
. |
---|---|
ISSN: | 0035-5038 1827-3491 |
DOI: | 10.1007/s11587-015-0240-1 |