  Let K be an algebraically closed field of characteristic p. We exhibit a
counterexample against a theorem asserted in one of our earlier papers, which
claims to characterize the integral closure of K((t)) within the field of
Hahn-Mal'cev-Neumann generalized power series. We then give a corrected
characterization, generalizing our earlier description in terms of finite
automata in the case where K is the algebraic closure of a finite field. We
also characterize the integral closure of K(t), thus generalizing a well-known
theorem of Christol and suggesting a possible framework for computing in this
integral closure. We recover various corollaries on the structure of algebraic
generalized power series; one of these is an extension of Derksen's theorem on
the zero sets of linear recurrent sequences in characteristic $p$.
