Minimal approximations, orbital elementary modules, and orbit algebras of regular modules (Q1305010)

\textit{W. Crawley-Boevey} and \textit{O. Kerner} [Math. Ann. 298, No. 3, 481-487 (1994; Zbl 0793.16005)], have introduced a functor between categories of regular modules for wild hereditary algebras. Here, the author continues the study of this functor giving in particular a description of it without the use of direct limits. This can be done by considering the so-called minimal approximations. This description has the following consequence. It creates a new class of elementary modules called by the author orbital elementary and which satisfy the following property: if \(E\) is orbital elementary, then it is possible to describe all maps between the modules in the \(\tau_A\)-orbit of \(E\).