Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Noetherian operators, primary submodules and symbolic powers   We give an algebraic and self-contained proof of the existence of the
so-called Noetherian operators for primary submodules over general classes of
Noetherian commutative rings. The existence of Noetherian operators accounts to
provide an equivalent description of primary submodules in terms of
differential operators. As a consequence, we introduce a new notion of
differential powers which coincides with symbolic powers in many interesting
non-smooth settings, and so it could serve as a generalization of the
Zariski-Nagata Theorem.

23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph