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1999 | 81 | 1 | 21-31

Tytuł artykułu

Full embeddings of almost split sequences over split-by-nilpotent extensions

Treść / Zawartość

Języki publikacji

EN

Abstrakty

EN
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 $M ⊗ _A Q = 0$.

Rocznik

Tom

81

Numer

1

Strony

21-31

Daty

wydano
1999
otrzymano
1998-11-30
poprawiono
1998-12-10

Twórcy

  • 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

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  • [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.

Identyfikator YADDA

bwmeta1.element.bwnjournal-article-cmv81i1p21bwm