Valued Gabriel quiver of a wedge product and semiprime coalgebras

摘要

We make a first approach to the representation theory of the wedge product ofcoalgebras by means of the description of its valued Gabriel quiver. Then wedefine semiprime coalgebras and study its category of comodules by the use oflocalization techniques. In particular, we prove that, whether its Gabrielquiver is locally finite, any monomial semiprime fc-tame coalgebra is string.We also prove a weaker version of Eisenbud-Griffith theorem, namely, anyhereditary semiprime strictly quasi-finite coalgebra is serial.