Geodesic
On the Decomposition of Nonsingular CS-Modules
Canadian mathematical bulletin, Tome 39 (1996) no. 3, pp. 257-265

Voir la notice de l'article provenant de la source Cambridge

DOI

It is shown that if M is a nonsingular CS-module with an indecomposable decomposition M = ⊕i∊I Mi , then the family {Mi | i € I} is locally semi-T"- nilpotent. This fact is used to prove that any nonsingular self-generator Σ-CS module is a direct sum of uniserial Noetherian quasi-injective submodules. As an application, we provide a new proof of Goodearl's characterization of non-singular rings over which all nonsingular right modules are projective.
DOI : 10.4153/CMB-1996-033-4
Mots-clés : Primary: 16D70, secondary: 16D40, 16D50, 16D80, nonsingular module, CS-module, indecomposable module, quasi-injective module, uniserial module, hereditary ring 
Clark, John; Dung, Nguyen Viet. On the Decomposition of Nonsingular CS-Modules. Canadian mathematical bulletin, Tome 39 (1996) no. 3, pp. 257-265. doi: 10.4153/CMB-1996-033-4
@article{10_4153_CMB_1996_033_4,
     author = {Clark, John and Dung, Nguyen Viet},
     title = {On the {Decomposition} of {Nonsingular} {CS-Modules}},
     journal = {Canadian mathematical bulletin},
     pages = {257--265},
     year = {1996},
     volume = {39},
     number = {3},
     doi = {10.4153/CMB-1996-033-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1996-033-4/}
}
TY  - JOUR
AU  - Clark, John
AU  - Dung, Nguyen Viet
TI  - On the Decomposition of Nonsingular CS-Modules
JO  - Canadian mathematical bulletin
PY  - 1996
SP  - 257
EP  - 265
VL  - 39
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1996-033-4/
DO  - 10.4153/CMB-1996-033-4
ID  - 10_4153_CMB_1996_033_4
ER  - 
%0 Journal Article
%A Clark, John
%A Dung, Nguyen Viet
%T On the Decomposition of Nonsingular CS-Modules
%J Canadian mathematical bulletin
%D 1996
%P 257-265
%V 39
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1996-033-4/
%R 10.4153/CMB-1996-033-4
%F 10_4153_CMB_1996_033_4

Cité par Sources :