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

100%
Assem I., Zacharia D.
Colloquium Mathematicum
|
1999
|
tom 81
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nr 1
21-31
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 $M ⊗ _A Q = 0$.
2
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On split-by-nilpotent extensions

100%
Assem I., Zacharia D.
Colloquium Mathematicum
|
2003
|
tom 98
|
nr 2
259-275
EN
Let A and R be two artin algebras such that R is a split extension of A by a nilpotent ideal. We prove that if R is quasi-tilted, or tame and tilted, then so is A. Moreover, generalizations of these properties, such as laura and shod, are also inherited. We also study the relationship between the tilting R-modules and the tilting A-modules.
3
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Finiteness of the strong global dimension of radical square zero algebras

81%
Kerner O., Skowroński A., Yamagata K., Zacharia D.
Open Mathematics
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2004
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tom 2
|
nr 1
103-111
EN
The strong global dimension of a finite dimensional algebra A is the maximum of the width of indecomposable bounded differential complexes of finite dimensional projective A-modules. We prove that the strong global dimension of a finite dimensional radical square zero algebra A over an algebraically closed field is finite if and only if A is piecewise hereditary. Moreover, we discuss results concerning the finiteness of the strong global dimension of algebras and the related problem on the density of the push-down functors associated to the canonical Galois coverings of the trivial extensions of algebras by their repetitive algebras.
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