Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tensor-Multinomial Sums of Ideals: Primary Decompositions and
  Persistence of Associated Primes   Given a polynomial ring $C$ over a field and proper ideals $I$ and $J$ whose
generating sets involve disjoint variables, we determine how to embed the
associated primes of each power of $I+J$ into a collection of primes described
in terms of the associated primes of select powers of $I$ and of $J$. We record
two applications. First, in case the field is algebraically closed, we
construct primary decompositions for powers of $I+J$ from primary
decompositions for powers of $I$ and $J$. Separately, we attack the persistence
problem for associated primes of powers of an ideal in case one of $I$ or $J$
is a non-zero normal ideal.

0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th