Linear maps of holomorphic functions on commutative algebras

Generalized function theory on finite dimensional linear associative algebras over the fieldo freals has pro- duced many forms o f generalized regular1ty Of particularin - terest are the forms o fregularity known as S-regularity and F- regularity. It is well known that functions regular in one sense need not be regular in the other. Here we prove a transformation theorem which allows the formation o f F-regular functions from S- regular functions. Furthermore, a classi flcation theorem is proved that determines the algebras for which this transformation property holds.