  We construct an algebra of generalized functions endowed with a canonical
embedding of the space of Schwartz distributions. We offer a solution to the
problem of multiplication of Schwartz distributions similar to but different
from Colombeau's solution. We show that the set of scalars of our algebra is an
algebraically closed field unlike its counterpart in Colombeau theory, which is
a ring with zero divisors. We prove a Hahn-Banach extension principle which
does not hold in Colombeau theory. We establish a connection between our theory
with non-standard analysis and thus answer, although indirectly, a question
raised by J.F. Colombeau. This article provides a bridge between Colombeau
theory of generalized functions and non-standard analysis.
