Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear maps on k^I, and homomorphic images of infinite direct product
  algebras   Let k be an infinite field, I an infinite set, V a k-vector-space, and
g:k^I\to V a k-linear map. It is shown that if dim_k(V) is not too large (under
various hypotheses on card(k) and card(I), if it is finite, respectively
countable, respectively < card(k)), then ker(g) must contain elements
(u_i)_{i\in I} with all but finitely many components u_i nonzero.
  These results are used to prove that any homomorphism from a direct product
\prod_I A_i of not-necessarily-associative algebras A_i onto an algebra B,
where dim_k(B) is not too large (in the same senses) must factor through the
projection of \prod_I A_i onto the product of finitely many of the A_i, modulo
a map into the subalgebra \{b\in B | bB=Bb=\{0\}\}\subseteq B.
  Detailed consequences are noted in the case where the A_i are Lie algebras.

12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs