@article{Tachikawa2009,
abstract = {We prove that an associated graded algebra $R_G$ of a finite dimensional algebra $R$ is $QF$ (= selfinjective) if and only if $R$ is $QF$ and Loewy coincident. Here $R$ is said to be Loewy coincident if, for every primitive idempotent $e$, the upper Loewy series and the lower Loewy series of $Re$ and $eR$ coincide. $QF$-3 algebras are an important generalization of $QF$ algebras; note that Auslander algebras form a special class of these algebras. We prove that for a Loewy coincident algebra $R$, the associated graded algebra $R_G$ is $QF$-3 if and only if $R$ is $QF$-3.},
author = {Tachikawa, Hiroyuki},
journal = {Czechoslovak Mathematical Journal},
keywords = {associated graded algebra; $QF$ algebra; $QF$-3 algebra; upper Loewy series; lower Loewy series; associated graded algebra; algebra; -3 algebra; upper Loewy series; lower Loewy series},
language = {eng},
number = {3},
pages = {583-589},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Loewy coincident algebra and $QF$-3 associated graded algebra},
url = {http://eudml.org/doc/37943},
volume = {59},
year = {2009},
}
TY - JOUR
AU - Tachikawa, Hiroyuki
TI - Loewy coincident algebra and $QF$-3 associated graded algebra
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 3
SP - 583
EP - 589
AB - We prove that an associated graded algebra $R_G$ of a finite dimensional algebra $R$ is $QF$ (= selfinjective) if and only if $R$ is $QF$ and Loewy coincident. Here $R$ is said to be Loewy coincident if, for every primitive idempotent $e$, the upper Loewy series and the lower Loewy series of $Re$ and $eR$ coincide. $QF$-3 algebras are an important generalization of $QF$ algebras; note that Auslander algebras form a special class of these algebras. We prove that for a Loewy coincident algebra $R$, the associated graded algebra $R_G$ is $QF$-3 if and only if $R$ is $QF$-3.
LA - eng
KW - associated graded algebra; $QF$ algebra; $QF$-3 algebra; upper Loewy series; lower Loewy series; associated graded algebra; algebra; -3 algebra; upper Loewy series; lower Loewy series
UR - http://eudml.org/doc/37943
ER -