Localization in right (*)-serial coalgebras. (Q610732)

Let \(C\) be a coalgebra. A right \(C\)-comodule is uniserial if its lattice of subcomodules is a chain. It is biserial if there are only two maximal chains in the lattice of subcomodules. \(C\) is called right \((*)\)-serial if its right injective indecomposable comodules are uniserial or biserial. \((*)\)-serial coalgebras are characterized using localization techniques: \(C\) is right \((*)\)-serial if and only if each socle-finite localized coalgebra of \(C\) is right \((*)\)-serial.