On hereditary rings and the pure semisimplicity conjecture II: Sporadic potential counterexamples

José L. García. "On hereditary rings and the pure semisimplicity conjecture II: Sporadic potential counterexamples." Colloquium Mathematicae 139.1 (2015): 55-93. <http://eudml.org/doc/283484>.

@article{JoséL2015,
abstract = {It was shown in [Colloq. Math. 135 (2014), 227-262] that the pure semisimplicity conjecture (briefly, pssC) can be split into two parts: first, a weak pssC that can be seen as a purely linear algebra condition, related to an embedding of division rings and properties of matrices over those rings; the second part is the assertion that the class of left pure semisimple sporadic rings (ibid.) is empty. In the present article, we characterize the class of left pure semisimple sporadic rings having finitely many Auslander-Reiten components; the characterization is given through properties of the defining bimodules and the sequences of dimensions associated to these bimodules.},
author = {José L. García},
journal = {Colloquium Mathematicae},
keywords = {pure semisimple rings; pure semisimplicity conjecture; finite representation type; sporadic rings; dimension sequences; Auslander-Reiten components; tilting modules; direct sums of finitely generated modules; triangular matrix rings},
language = {eng},
number = {1},
pages = {55-93},
title = {On hereditary rings and the pure semisimplicity conjecture II: Sporadic potential counterexamples},
url = {http://eudml.org/doc/283484},
volume = {139},
year = {2015},
}

TY - JOUR
AU - José L. García
TI - On hereditary rings and the pure semisimplicity conjecture II: Sporadic potential counterexamples
JO - Colloquium Mathematicae
PY - 2015
VL - 139
IS - 1
SP - 55
EP - 93
AB - It was shown in [Colloq. Math. 135 (2014), 227-262] that the pure semisimplicity conjecture (briefly, pssC) can be split into two parts: first, a weak pssC that can be seen as a purely linear algebra condition, related to an embedding of division rings and properties of matrices over those rings; the second part is the assertion that the class of left pure semisimple sporadic rings (ibid.) is empty. In the present article, we characterize the class of left pure semisimple sporadic rings having finitely many Auslander-Reiten components; the characterization is given through properties of the defining bimodules and the sequences of dimensions associated to these bimodules.
LA - eng
KW - pure semisimple rings; pure semisimplicity conjecture; finite representation type; sporadic rings; dimension sequences; Auslander-Reiten components; tilting modules; direct sums of finitely generated modules; triangular matrix rings
UR - http://eudml.org/doc/283484
ER -