  We study quasi-Hopf algebras and their subobjects over certain commutative
rings from the point of view of Frobenius algebras. We introduce a type of
Radford formula involving an anti-automorphism and the Nakayama automorphism of
a Frobenius algebra, then view several results in quantum algebras from this
vantage-point. In addition, separability and strong separability of quasi-Hopf
algebras are studied as Frobenius algebras.
