The valued Gabriel quiver of a wedge product and semiprime coalgebras

Abstract

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