Strong no-loop conjecture for algebras with two simples and radical cube zero

Bernt T. Jensen. "Strong no-loop conjecture for algebras with two simples and radical cube zero." Colloquium Mathematicae 102.1 (2005): 1-7. <http://eudml.org/doc/284042>.

@article{BerntT2005,
abstract = {Let Λ be an artinian ring and let 𝔯 denote its Jacobson radical. We show that a simple module of finite projective dimension has no self-extensions when Λ is graded by its radical, with at most two simple modules and 𝔯⁴ = 0, in particular, when Λ is a finite-dimensional algebra over an algebraically closed field with at most two simple modules and 𝔯³ = 0.},
author = {Bernt T. Jensen},
journal = {Colloquium Mathematicae},
keywords = {Artinian rings; rings graded by radicals; projective dimension; Cartan determinants; simple modules; no-loop conjecture; finite-dimensional algebras},
language = {eng},
number = {1},
pages = {1-7},
title = {Strong no-loop conjecture for algebras with two simples and radical cube zero},
url = {http://eudml.org/doc/284042},
volume = {102},
year = {2005},
}

TY - JOUR
AU - Bernt T. Jensen
TI - Strong no-loop conjecture for algebras with two simples and radical cube zero
JO - Colloquium Mathematicae
PY - 2005
VL - 102
IS - 1
SP - 1
EP - 7
AB - Let Λ be an artinian ring and let 𝔯 denote its Jacobson radical. We show that a simple module of finite projective dimension has no self-extensions when Λ is graded by its radical, with at most two simple modules and 𝔯⁴ = 0, in particular, when Λ is a finite-dimensional algebra over an algebraically closed field with at most two simple modules and 𝔯³ = 0.
LA - eng
KW - Artinian rings; rings graded by radicals; projective dimension; Cartan determinants; simple modules; no-loop conjecture; finite-dimensional algebras
UR - http://eudml.org/doc/284042
ER -