Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The images of some simple derivations   In the paper, we study the relation between the images of polynomial
derivations and their simplicity. We prove that the images of simple Shamsuddin
derivations are not Mathieu-Zhao spaces. In addition, we also show that the
images of some simple derivations in dimension three are not Mathieu-Zhao
spaces. Thus, we conjecture that the images of simple derivations in dimension
greater than one are not Mathieu-Zhao spaces. We also prove that locally
nilpotent derivations are not simple in dimension greater than one.

5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int