Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the image of polynomials evaluated on incidence algebras: a
  counter-example and a solution   In this paper, we investigate the subset obtained by evaluations of a fixed
multilinear polynomial on a given algebra. We provide an example of a
multilinear polynomial, whose image is not a vector subspace; namely, the
product of two commutators need not to be a subspace whenever evaluated on
certain subalgebras of upper triangular matrices (the so-called incidence
algebras).
  In the last part of the paper, given that the field is infinite, we reduce
the problem of the description of the image of a polynomial evaluated on an
incidence algebra to the study of evaluations of a certain family of
polynomials on its Jacobson radical. In particular, we are able to describe the
image of multilinear polynomials evaluated on the algebra of upper triangular
matrices.

21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th