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

Ibrahim Assem; Dan Zacharia

Colloquium Mathematicae (1999)

  • Volume: 81, Issue: 1, page 21-31
  • ISSN: 0010-1354

Abstract

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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 H o m A ( Q , τ A M ) = 0 and M ⊗ A Q = 0 .

How to cite

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Assem, Ibrahim, and Zacharia, Dan. "Full embeddings of almost split sequences over split-by-nilpotent extensions." Colloquium Mathematicae 81.1 (1999): 21-31. <http://eudml.org/doc/210727>.

@article{Assem1999,
abstract = {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 $M ⊗ _A Q = 0$.},
author = {Assem, Ibrahim, Zacharia, Dan},
journal = {Colloquium Mathematicae},
keywords = {Auslan-der-Reiten translate; split-by-nilpotent extension; almost split sequence; split-by-nilpotent extensions; almost split sequences; Auslander-Reiten translates; Artin algebras},
language = {eng},
number = {1},
pages = {21-31},
title = {Full embeddings of almost split sequences over split-by-nilpotent extensions},
url = {http://eudml.org/doc/210727},
volume = {81},
year = {1999},
}

TY - JOUR
AU - Assem, Ibrahim
AU - Zacharia, Dan
TI - Full embeddings of almost split sequences over split-by-nilpotent extensions
JO - Colloquium Mathematicae
PY - 1999
VL - 81
IS - 1
SP - 21
EP - 31
AB - 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 $M ⊗ _A Q = 0$.
LA - eng
KW - Auslan-der-Reiten translate; split-by-nilpotent extension; almost split sequence; split-by-nilpotent extensions; almost split sequences; Auslander-Reiten translates; Artin algebras
UR - http://eudml.org/doc/210727
ER -

References

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  9. [9] N. Marmaridis, On extensions of abelian categories with applications to ring theory, J. Algebra 156 (1993), 50-64. Zbl0796.18007
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  13. [13] K. Yamagata, Extensions over hereditary artinian rings with self-dualities I, J. Algebra 73 (1981), 386-433. Zbl0471.16022

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