Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Attached primes of the top local cohomology modules with respect to an
  ideal (II)   For a finitely generated module $M$, over a commutative Noetherian local ring
$(R, \mathfrak{m})$, it is shown that there exist only a finite number of
non--isomorphic top local cohomology modules
$\mathrm{H}_{\mathfrak{a}}^{\mathrm{dim} (M)}(M)$, for all ideals
$\mathfrak{a}$ of $R$. We present a reduced secondary representation for the
top local cohomology modules with respect to an ideal. It is also shown that
for a given integer $r\geq 0$, if $\mathrm{H}_{\mathfrak{a}}^{r}(R/\mathfrak
{p})$ is zero for all $\mathfrak{p}$ in $\mathrm{Supp}(M)$, then
$\mathrm{H}_{\mathfrak{a}}^{i}(M)= 0$ for all $i\geq r$.

13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys