1997 | OriginalPaper | Buchkapitel
Co— Versus Contravariant Finiteness of Categories of Representations
verfasst von : B. Huisgen-Zimmermann, S. O. Smalø
Erschienen in: Advances in Ring Theory
Verlag: Birkhäuser Boston
Enthalten in: Professional Book Archive
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
This article supplements recent work of the authors. (1) A criterion for failure of covariant finiteness of a full subcategory of Λ-mod is given, where Λ is a finite dimensional algebra. The criterion is applied to the category P∞ (Λ-mod) of all finitely generated Λ-modules of finite projective dimension, yielding a negative answer to the question whether P∞ (Λ-mod) is always covariantly finite in Λ-mod. Part (2) concerns contravariant finiteness of P∞ (Λ-mod). An example is given where this condition fails, the failure being, however, curable via a sequence of one-point extensions. In particular, this example demonstrates that curing failure of contravariant finiteness of P∞ (Λ-mod) usually involves a tradeoff with respect to other desirable qualities of the algebra.