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

Volume 139 / 2015

José L. García Colloquium Mathematicum 139 (2015), 55-93 MSC: Primary 16G60. DOI: 10.4064/cm139-1-4

Abstract

$\hskip -1pt$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.

Authors

  • José L. GarcíaDepartment of Mathematics
    University of Murcia
    30100 Murcia, Spain
    e-mail

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