  The theory of algebraic extensions of Banach algebras is well established,
and there are many constructions which yield interesting extensions. In
particular, Cole's method for extending uniform algebras by adding square roots
of functions to a given uniform algebra has been used to solve many problems
within uniform algebra theory. However, there are numerous other examples in
the theory of uniform algebras that can be realised as extensions of a uniform
algebra, and these more general extensions have received little attention in
the literature. In this paper, we investigate more general classes of uniform
algebra extensions. We introduce a new class of extensions of uniform algebras,
and show that several important properties of the original uniform algebra are
preserved in these extensions. We also show that several well-known examples
from the theory of uniform algebras belong to these more general classes of
uniform algebra extensions.
