Stable equivalence of artin algebras

Picard Groups, Grothendieck Rings, and Burnside Rings of Categories

Endlich präsentierbare Moduln

This paper deals with the representation theory of strongly locally finite quivers. We first study some properties of the finitely presented or copresented representations, and then construct in the category of locally finite dimensional representations some almost split sequences which start with a finitely co-presented representation and end with a finitely presented representation. Furthermore, we obtain a general description of the shapes of the Auslander-Reiten components of the category of finitely presented representations and prove that the number of regular Auslander-Reiten components is infinite if and only if the quiver is not of finite or infinite Dynkin type. In the infinite Dynkin case, we shall give a complete list of the indecomposable representations and an explicit description of the Auslander-Reiten components. Finally, we apply these results to study the Auslander-Reiten theory in the derived category of bounded complexes of finitely presented representations. 2010 Mathematics Subject Classification: 16G20; 16G70.

Representation theory of strongly locally finite quivers

We show that for a finitely generated module M over a complete intersection R, the vanishing of for a certain number of consecutive values of i starting at n forces the projective dimension of M to be at most n − 1. In particular, if and only if the projective dimension of M over R is at most one. We also verify a conjecture of Auslander and Reiten for modules over commutative rings with certain typical behaviors, which augments the recent literature.

Finite projective dimension and the vanishing of extR(M, M)

Proceedings of the Conference on Categorical Algebra, La Jolla 1965. VIII + 562 S. Berlin/Heidelberg/New York 1966. Springer-Verlag. Preis geb. DM 58, - .

M. Hasse

Papers

Proceedings of the Conference on Categorical Algebra, La Jolla 1965. VIII + 562 S. Berlin/Heidelberg/New York 1966. Springer-Verlag. Preis geb. DM 58, - .