Abstract
We determine all indecomposable injective diagrams over a poset I with values in some category R-Mod of modules and characterize the case when every injective diagram decomposes into a direct sum of indecomposables. Moreover, we show that injective diagrams have a standard form dual to that of projective diagrams iff I is a noetherian poset.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
F. Anderson and K. Fuller: Rings and Categories of Modules. Springer-Verlag, Berlin, 1973
M. Höppner and H. Lenzing: Projective diagrams over partially ordered sets are free. J. pure appl. Alg. 20 (1981) 7–12
M. Höppner and H. Lenzing: Diagrams over ordered sets: A simple model of abelian group theory. Abelian Group Theory (ed. R. Göbel and E. Walker), Springer LNM 874 (1981) 417–430
B. Mitchell: Rings with several objects. Advances Math. 8 (1972) 1–161
B. Mitchell: Some applications of module theory to functor categories. Bull. Amer. Math. Soc. 84 (1978) 867–885
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Höppner, M. A note on the structure of injective diagrams. Manuscripta Math 44, 45–50 (1983). https://doi.org/10.1007/BF01166072
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01166072