Serial coalgebras and their valued Gabriel quivers

Details Serial coalgebras and their valued Gabriel quivers Serial coalgebras and their valued Gabriel quivers

2007-07-01

arxiv.org/abs/0707.0132v1

Mathematics

Representation Theory

22 pages

Scientific paper

We study serial coalgebras by means of their valued Gabriel quivers. In particular, Hom-computable and representation-directed coalgebras are characterized. The Auslander-Reiten quiver of a serial coalgebra is described. Finally, a version of Eisenbud-Griffith theorem is proved, namely, every subcoalgebra of a prime, hereditary and strictly quasi-finite coalgebra is serial.

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