Valued Gabriel quiver of a wedge product and semiprime coalgebras

摘要

We describe the valued Gabriel quiver of a wedge product of coalgebras and study the category of comodules of a semiprime coalgebra. In particular, we prove that any monomial semiprime k-tame fc-tame coalgebra is string. We also prove a version of Eisenbud-Grimth theorem for coalgebras, namely, any hereditary semiprime strictly quasi-finite coalgebra is serial.