\textit{V. Geffert} [Theor. Comput. Sci. 62, 235-249 (1988; Zbl 0664.68075)] has shown that each recursively enumerable language L over \(\Sigma\) can be expressed in the form \(L=\{h(x)^{-1}g(x)|\) x in \(\Delta^+\}\cap \Sigma^*\) where \(\Delta\) is an alphabet and g, h is a pair of morphisms. Our purpose is to give a simple proof for Geffert's result and then sharpen it into the form where both of the morphisms are nonerasing. In our method we modify constructions used in a representation of recursively enumerable languages in terms of equality sets and in a characterization of simple transducers in terms of morphisms. As direct consequences, we get the undecidability of the Post correspondence problem and various representations of L. For instance, \(L=\rho (L_ 0)\cap \Sigma^*\) where \(L_ 0\) is a minimal linear language and \(\rho\) is the Dyck reduction \(a\bar a\to \epsilon\), \(A\bar A\to \epsilon\).