Z₃×Z₃ crossed products

Let A be the generic abelian crossed product with respect to Z₃×Z₃. 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 [9] to prove that if A is any algebra of degree 9 then A is similar to the product of 35. 840 symbol algebras (8960 of degree 3 and 26. 880 of degree 9) and if A is of exponent 3 it is similar to the product of 277. 760 symbol algebras of degree 3. We then show that the essential 3-dimension of the class of A is at most 6.