Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
Let R be a split extension of an artin algebra A by a nilpotent bimodule $_A Q_A$, and let M be an indecomposable non-projective A-module. We show that the almost split sequences ending with M in mod A and mod R coincide if and only if $Hom_A (Q, τ_A M)$ = 0 and $M ⊗ _A Q = 0$.
Czasopismo
Rocznik
Tom
Numer
Strony
21-31
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-11-30
poprawiono
1998-12-10
Twórcy
autor
- Département de mathématiques et d'informatique, Université de Sherbrooke, Sherbrooke, Québec, J1K 2R1 Canada
autor
- Department of Mathematics, Syracuse University, Syracuse, NY 13244, U.S.A.
Bibliografia
- [1] I. Assem and F. U. Coelho, Glueings of tilted algebras, J. Pure Appl. Algebra 96 (1994), 225-243.
- [2] I. Assem and N. Marmaridis, Tilting modules over split-by-nilpotent extensions, Comm. Algebra 26 (1998), 1547-1555.
- [3] M. Auslander and I. Reiten, Representation theory of artin algebras V, ibid. 5 (1997), 519-554.
- [4] M. Auslander, I. Reiten and S. O. Smalο, Representation Theory of Artin Algebras, Cambridge Univ. Press, 1995.
- [5] K. R. Fuller, *-Modules over ring extensions, Comm. Algebra 25 (1997), 2839-2860.
- [6] D. Happel, Triangulated Categories in the Representation Theory of Finite Dimensional Algebras, London Math. Soc. Lecture Note Ser. 119, Cambridge Univ. Press, 1998.
- [7] M. Hoshino, Trivial extensions of tilted algebras, Comm. Algebra 10 (1982), 1965-1999.
- [8] D. Hughes and J. Waschbüsch, Trivial extensions of tilted algebras, Proc. London Math. Soc. 46 (1983), 347-364.
- [9] N. Marmaridis, On extensions of abelian categories with applications to ring theory, J. Algebra 156 (1993), 50-64.
- [10] C. M. Ringel, Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math. 1099, Springer, 1984.
- [11] A. Skowroński, Minimal representation-infinite artin algebras, Math. Proc. Cambridge Philos. Soc. 116 (1994), 229-243.
- [12] H. Tachikawa, Representations of trivial extensions of hereditary algebras, in: Lecture Notes in Math. 832, Springer, 1980, 579-599.
- [13] K. Yamagata, Extensions over hereditary artinian rings with self-dualities I, J. Algebra 73 (1981), 386-433.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv81i1p21bwm