Geodesic
Infinite rank representations of orders in nonsemisimple algebras, and module categories
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 3, pp. 173-187
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Let $R$ be a Dedekind domain with quotient field $K$ and let $\Lambda$ be an $R$-order in a finite-dimensional $K$-algebra $A$ such that $A/\operatorname{Rad}A$ is separable. We show that if $A$ is not semisimple, then there exists a maximal $R$-order $\Delta$ in a skew-field such that the category $\Lambda\text{-}\mathbf{Lat}$ of $R$-projective $\Lambda$-modules admits a full module category $\Delta\text{-}\mathbf{Mod}$ as a subfactor. 
@article{FPM_2005_11_3_a11,
     author = {W. Rump},
     title = {Infinite rank representations of orders in nonsemisimple algebras, and module categories},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {173--187},
     year = {2005},
     volume = {11},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2005_11_3_a11/}
}
TY  - JOUR
AU  - W. Rump
TI  - Infinite rank representations of orders in nonsemisimple algebras, and module categories
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2005
SP  - 173
EP  - 187
VL  - 11
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/FPM_2005_11_3_a11/
LA  - ru
ID  - FPM_2005_11_3_a11
ER  - 
%0 Journal Article
%A W. Rump
%T Infinite rank representations of orders in nonsemisimple algebras, and module categories
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2005
%P 173-187
%V 11
%N 3
%U http://geodesic.mathdoc.fr/item/FPM_2005_11_3_a11/
%G ru
%F FPM_2005_11_3_a11
W. Rump. Infinite rank representations of orders in nonsemisimple algebras, and module categories. Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 3, pp. 173-187. http://geodesic.mathdoc.fr/item/FPM_2005_11_3_a11/

[1] Fuks L., Beskonechnye abelevy gruppy, T. 2, Mir, M., 1977

[2] Anderson F. W., Fuller K. R., Rings and Categories of Modules, Springer, Berlin, 1974 | MR

[3] Auslander M., Large Modules over Artin Algebras, Algebra, Topology, and Category Theory, A Collection of Papers in Honor of Samuel Eilenberg, Academic Press, London, 1976 | MR

[4] Butler M. C. R., Campbell J. M., Kovács L. G., “On infinite rank integral representations of groups and orders of finite lattice type”, Arch. Math. (to appear)

[5] Crawley-Boevey W., “Infinite-dimensional modules in the representation theory of finite-dimensional algebras. Trondheim lectures (1996)”, Algebras and Modules, I, CMS Conference Proceedings 23, Providence, 1998, 29–54 | MR | Zbl

[6] Curtis C. W., Reiner I., Methods of Representation Theory, II, John Wiley and Sons, New York, 1987 | MR | Zbl

[7] MacLane S., Categories for the Working Mathematician, Springer, New York, 1971 | MR | Zbl

[8] Reiner I, Maximal Orders, London Math. Society Monographs. New series, 28, Oxford University Press, Oxford, 2003 | MR | Zbl

[9] Ringel C. M., “Infinite length modules. Some examples as introduction”, Infinite Length Modules, eds. H. Krause, C. M. Ringel, Birkhäuser, 2000, 1–73 | MR | Zbl

[10] Rump W., Almost Fully Decomposable Infinite Rank Lattices over Orders, Preprint, 2004 | MR

[11] Rump W., “Large indecomposables over representation-infinite orders and algebras”, Arch. Math. (to appear)

[12] Rump W., “Large lattices over orders”, Proc. London Math. Soc. (to appear) | DOI