Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $\mathbb{Z}_3\times \mathbb{Z}_3$ crossed products   Let $A$ be the generic abelian crossed product with respect to
$\mathbb{Z}_3\times \mathbb{Z}_3$, in this note we show that $A$ is similar to
the tensor product of 4 symbol algebras (3 of degree 9 and one of degree 3) and
if $A$ is of exponent $3$ it is similar to the product of 31 symbol algebras of
degree $3$. We then use \cite{RS} to prove that if $A$ is any algebra of degree
$9$ then $A$ is similar to the product of $35840$ symbol algebras ($8960$ of
degree $3$ and $26880$ of degree $9$) and if $A$ is of exponent $3$ it is
similar to the product of $277760$ symbol algebras of degree $3$. We then show
that the essential $3$-dimension of the class of $A$ is at most $6$.

21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph