Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Embeddings of fields into simple algebras: generalizations and
  applications   For two semi-simple algebras $A$ and $B$ over an arbitrary ground field $F$,
we give a numerical criterion when $\Hom_F(A,B)$, the set of $F$-algebra
homomorphisms between them, is non-empty. We also determine when the orbit set
$B^\times \backslash \Hom_\falg(A,B)$ is finite and give an explicit formula
for its cardinality. A few applications of main results are given.

23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat