Geodesic
Torsion Theories Induced by Tilting Modules
Canadian journal of mathematics, Tome 36 (1984) no. 5, pp. 899-913

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

Let k be a commutative field, and A a finite-dimensional k-algebra. By a module will always be meant a finitely generated right module. Following [8], we shall call a module TA a tilting module if (1) pdTA ≦ 1, (2) Ext1 A (T, T) = 0 and (3) there is a short exact sequence with T’ and T” direct sums of direct summands of T. Given a tilting module TA, the full subcategories and of the category modA of A -modules are respectively the torsion-free class and the torsion class of a torsion theory on modA[8]. The aim of the present paper is to find conditions on a torsion theory in order that it be induced by a tilting module. 
Assem, Ibrahim. Torsion Theories Induced by Tilting Modules. Canadian journal of mathematics, Tome 36 (1984) no. 5, pp. 899-913. doi: 10.4153/CJM-1984-051-5
@article{10_4153_CJM_1984_051_5,
     author = {Assem, Ibrahim},
     title = {Torsion {Theories} {Induced} by {Tilting} {Modules}},
     journal = {Canadian journal of mathematics},
     pages = {899--913},
     year = {1984},
     volume = {36},
     number = {5},
     doi = {10.4153/CJM-1984-051-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1984-051-5/}
}
TY  - JOUR
AU  - Assem, Ibrahim
TI  - Torsion Theories Induced by Tilting Modules
JO  - Canadian journal of mathematics
PY  - 1984
SP  - 899
EP  - 913
VL  - 36
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1984-051-5/
DO  - 10.4153/CJM-1984-051-5
ID  - 10_4153_CJM_1984_051_5
ER  - 
%0 Journal Article
%A Assem, Ibrahim
%T Torsion Theories Induced by Tilting Modules
%J Canadian journal of mathematics
%D 1984
%P 899-913
%V 36
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1984-051-5/
%R 10.4153/CJM-1984-051-5
%F 10_4153_CJM_1984_051_5

[1] 1. Assem, I. and Happel, D., Generalized tilted algebras of Type A , Comm. Algebra 9 (1981), 2101–2125. Google Scholar

[2] 2. Auslander, M. and Reiten, I., Representation theory of art in algebras III and IV, Comm. Algebra 3 (1975), 239–294 and 5 (1977), 443–518. Google Scholar

[3] 3. Auslander, M., Platzeck, M. I. and Reiten, I., Coxeter functors without diagrams, Trans. Amer Math. Soc. 250 (1979), 1–46. Google Scholar

[4] 4. Auslander, M. and Smalø, S. O., Preprojective modules over art in algebras, J. Algebra 66 (1980), 61–122. Google Scholar

[5] 5. Auslander, M. and Smalø, S. O., Almost split sequences in subcategories, J. Algebra 69 (1981), 426–454. Google Scholar

[6] 6. Auslander, M. and Smalø, S. O., Addendum to almost split sequences in subcategories, J. Algebra 71 (1981), 592–594. Google Scholar

[7] 7. Bongartz, K., Tilted algebras, Proc. ICRA III (1980), Springer Lecture Notes 903 (1982), 26–38. Google Scholar

[8] 8. Happel, D. and Ringel, C. M., Tilted algebras, Trans. Amer. Math. Soc. 274 (1982), 399–443. Google Scholar

[9] 9. Hoshino, M., On splitting torsion theories induced by tilting modules, Comm. Algebra 11 (1983), 427–440. Google Scholar

[10] 10. Hoshino, M., Tilting modules and torsion theories, Bull. London Math. Soc. 14 (1982), 334–336. Google Scholar

[11] 11. Ringel, C. M., Report on the Brauer-Thrall conjectures, Proc. ICRA II (1979), Springer Lecture Notes 831 (1980), 104–136. Google Scholar

[12] 12. Ringel, C. M., Tame algebras, Proc. ICRA II (1979), Springer Lecture Notes 831 (1980), 137–287. Google Scholar

[13] 13. Smalo, S. O., Torsion theories and tilting modules, preprint. Google Scholar | DOI

Cité par Sources :