  We propose an outgrowth of the expansion method introduced by de Azcarraga et
al. [Nucl. Phys. B 662 (2003) 185]. The basic idea consists in considering the
direct product between an abelian semigroup S and a Lie algebra g. General
conditions under which relevant subalgebras can systematically be extracted
from S \times g are given. We show how, for a particular choice of semigroup S,
the known cases of expanded algebras can be reobtained, while new ones arise
from different choices. Concrete examples, including the M algebra and a
D'Auria-Fre-like Superalgebra, are considered. Finally, we find explicit,
non-trace invariant tensors for these S-expanded algebras, which are essential
ingredients in, e.g., the formulation of Supergravity theories in arbitrary
space-time dimensions.
