  For an inclusion of C*-algebras $D\subseteq A$ with $D$ abelian, we show that
when $n\in A$ normalizes $D$, $n^*n$ and $nn^*$ commute with $D$. As a
corollary, when $D$ is a regular MASA in $A$, every approximate unit for $D$ is
also an approximate unit for $A$. This permits removal of the non-degeneracy
hypothesis from the definition of a Cartan MASA in the non-unital case.
  We give examples of singular MASA inclusions: for some, every approximate
unit for $D$ is an approximate unit for $A$, while for others, no approximate
unit for $D$ is an approximate unit for $A$. Our results imply that if the
unitization of an inclusion $D\subseteq A$ is a C*-diagonal, then $D$ is
regular in $A$. In contrast, we give an example of a non-regular inclusion
whose unitization is a Cartan inclusion.
  If $D$ is a MASA in $A$, we ask when $A$ is a subalgebra of $B$ with $D$ a
regular MASA in $B$. When $D$ is a MASA in $\mathcal B(\ell^2(\mathbb N))$, no
such $B$ exists.
