Can terms with different index structures be added in this equation?

[tetris11]

Homework Statement

Is this equation valid?

A_xy = B^z_zB_xz+ C_xyB_xyB^xy

The Attempt at a Solution

B^z_zB_xz = B^z_xz+z (I think)

C_xyB_xyB^xy = J^xy_2xy (I think)

so A_xy = B^z_xz+z + J^xy_2xy

My reasoning:
Since the two terms on the RHS do not share the same index structure, they cannot be added, and they do not share the same index structure with the LHS either.

So this equation is not possible, right?

 

[Hurkyl]

The problem with the equation is the serious grammatical error with the indices.

Assuming they were filled in correctly, it would depend upon what contractions were implicit in the notation. For example, the following is meaningful:

A_xy = B^z_yC_xz + D_uv E_xy F^uv​

 

[tetris11]

I don't really follow.
How does that contract?

In your example, would F^uv contract to something like J^k
And then would B^z contract to L (no upper indices?)

Would it be valid to say D_uvE_xyF^uv would contract to something like J^k_ab?