I have this beginner's question in Tensor Algebra:
Let's say we have two elements in the tensor algebra $T(V)$, where $V$ is a vector space, namely
$x_1\otimes\dots\otimes x_n$ and $y_1\otimes\dots\otimes y_m$.
When we multiply them together, do we get $$x_1\otimes\dots\otimes x_n\otimes y_1\otimes\dots\otimes y_m$$?
Thanks for any help.
Q2) A related question is when we multiply differential forms $x_1\wedge\dots\wedge x_n$ and $y_1\wedge\dots\wedge y_m$, do we get $$x_1\wedge\dots\wedge x_n\wedge y_1\wedge\dots\wedge y_m$$?