what is the tensor product $\mathbb{H\otimes_{R}H}$ I'm looking for a simpler way of thinking about the tensor product: $\mathbb{H\otimes_{R}H}$, i.e a more known algbera which is isomorphic to it.
I have built the algebra and played with it for a bit, but still can't seem to see any resemblence to anything i already know. 
Thanks!

Hint :
(1) Show that the map
$$H \otimes_R H \rightarrow End_R(H), x \otimes y \mapsto (a \mapsto xay).$$
is an isomorphism of $R$-vector spaces (I don't know the simplest way to do this, but try for example to look at a basis (dimension is 16...)).
(2) Denote by $H^{op}$ the $R$-algebra $H$ where the multiplication is reversed (i.e. $x \times_{H^{op}} y = y \times_{H} x$). Denote by (1,i,j,k) the usual basis. Show that the map
$$H \rightarrow H^{op}, 1 \mapsto 1,i \mapsto i, j \mapsto k, k \mapsto j$$ 
is an isomorphism of $R$-algebras
(3) Show that the map in (1)
$$H \otimes_R H^{op} \rightarrow End_R(H), x \otimes y \mapsto (a \mapsto xay).$$
is an isomophism of $R$-algebras
(4) Find an isomorphism $H \times_R H \rightarrow M_4(R)$ of $R$-algebras.
