  As a follow-up to work done in [7], some new insights to the structure of the
socle of a semisimple Banach algebra is obtained. In particular, it is shown
that the socle is isomorphic as an algebra to the direct sum of tensor products
of corresponding left and right minimal ideals. Remarkably, the
finite-dimensional case here reduces to the classical Wedderburn-Artin Theorem,
and this approach does not use any continuous irreducible representations of
the algebra in question. Furthermore, the structure of the socles for which the
classical Shoda's Theorem for matrices can be extended, is characterized
exactly as those socles which are minimal two-sided ideals. It is then shown
that the set of commutators in the socle (i.e. $\left\{xy-yx : x, y \in
\mathrm{Soc}\:A \right\}$) is a vector subspace. Finally, we characterize those
socles which belong to the center of a Banach algebra and obtain results which
suggests that the dimension of certain subalgebras of the socle in fact
provides a measure, to some extent, of commutativity.
