Valued Gabriel quiver of a wedge product and semiprime coalgebras

Abstract

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-Griffith theorem for coalgebras, namely, any hereditary semiprime strictly quasi-finite coalgebra is serial.

Key words： Wedge product; semiprime coalgebras; representation theory; valued Gabriel quiver

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