  The study of different types of ideals in non self-adjoint operator algebras
has been a topic of recent research. This study focuses on principal ideals in
subalgebras of groupoid C*-algebras. An ideal is said to be principal if it is
generated by a single element of the algebra. We look at subalgebras of
r-discrete principal groupoid C*-algebras and prove that these algebras are
principal ideal algebras. Regular canonical subalgebras of almost finite
C*-algebras have digraph algebras as their building blocks. The spectrum of
almost finite C*-algebras has the structure of an r-discrete principal groupoid
and this helps in the coordinization of these algebras. Regular canonical
subalgebras of almost finite C*-algebras have representations in terms of open
subsets of the spectrum for the enveloping C*-algebra. We conclude that regular
canonical subalgebras are principal ideal algebras.
