Abstract
In 1949, Mahler [9] started the study of rational approximation to algebraic elements in the field of power series with coefficients in a finite field, by adapting a classical theorem of Liouville concerning rational approximation to algebraic real numbers. In his paper, Mahler pointed at the difference with classical case by introducing an example. This example, having rational approximation reaching the Liouville's bound, proves that we haven't an analogue of Thue-Siegel-Roth theorem in positive characteristic. In this paper, we will prove that this example encompasses a large family of power series that are elements of Pisot and Salem retaining the same property of well approximation by the rationals. Further, we will discuss some Diophantine equations, closely related to these elements.