This is joint work with Florian Enescu. In this talk, we extend the definition of Frobenius complexity, introduce by Enescu and Yao, to the setting of Cartier sub-algebras. Furthermore, we show that, under suitable hypothesis, the Frobenius complexity is finite by showing an effective bound. As a corollary, we obtain a proof of the finiteness of the Frobenius Complexity of R for a large family of rings. Speaker(s): Felipe Perez (Georgia State University)