Serial coalgebras and their valued Gabriel quivers
J Gómez-Torrecillas, G Navarro - Journal of Algebra, 2008 - Elsevier
Journal of Algebra, 2008•Elsevier
We study serial coalgebras by means of their valued Gabriel quivers. In particular, Hom-
computable and representation-directed serial 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.
computable and representation-directed serial 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.
We study serial coalgebras by means of their valued Gabriel quivers. In particular, Hom-computable and representation-directed serial 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.
Elsevier
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