Lebesgue decomposition for representable functionals on ${}^{\ast }$-algebras

We present a Lebesgue-type decomposition for a representable functional on a ${}^{\ast }$-algebra into absolutely continuous and singular parts with respect to an other. This generalizes the corresponding results of S. P. Gudder for unital Banach ${}^{\ast }$-algebras. We also prove that the corresponding absolutely continuous parts are absolutely continuous with respect to each other.