When is a Coalgebra a Generator?

Let C be a coalgebra over a field k . The aim of this paper is to study the following problem : (P) If C is a k -coalgebra such that C is a generator for the category of left comodules, is C a left quasi-co-Frobenius coalgebra ? The converse always holds. We show that if C has a finite coradical ser...

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Veröffentlicht in:	Algebras and representation theory 2008-04, Vol.11 (2), p.179-190
Hauptverfasser:	Năstăsescu, C., Torrecillas, B., Van Oystaeyen, F.
Format:	Artikel
Sprache:	eng
Schlagworte:	Associative Rings and Algebras Commutative Rings and Algebras Mathematics Mathematics and Statistics Non-associative Rings and Algebras
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Beschreibung
Zusammenfassung:	Let C be a coalgebra over a field k . The aim of this paper is to study the following problem : (P) If C is a k -coalgebra such that C is a generator for the category of left comodules, is C a left quasi-co-Frobenius coalgebra ? The converse always holds. We show that if C has a finite coradical series, the answer is positive.
ISSN:	1386-923X 1572-9079
DOI:	10.1007/s10468-007-9054-5