On Finitely Generated and Projective Extensions of Banach Algebras

Abstract

We show that a finitely generated projective extension B of a commutative complex unitary Banach algebra A induces an open mapping $\pi$ between the carrier spaces. We next prove that if $\pi$ is a local homeomorphism then B contains an inertial subalgebra. Finally we present a necessary and sufficient condition for B to be uniform if A is.