  The theory of slice regular functions over the quaternions, introduced by
Gentili and Struppa in [5], was born on domains that intersect the real axis.
This hypothesis can be overcome using the theory of stem functions introduced
by Ghiloni and Perotti ([6]), in the context of real alternative algebras. In
this paper I will recall the notion and the main properties of stem functions.
After that I will introduce the class of slice regular functions induced by
stem functions and, in this set, I will extend the identity principle, the
maximum and minimum modulus principles and the open mapping theorem.
Differences will be shown between the case when the domain does or does not
intersect the real axis.
