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

• Autorzy: José L. García
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 16G60: Representation type (finite, tame, wild, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2015
• Tom: 139
• Numer: 1
• Strony: 55-93

Daty

wydano

2015

Twórcy

autor

José L. García

• Department of Mathematics, University of Murcia, 30100 Murcia, Spain

Identyfikatory

DOI

10.4064/cm139-1-4