Finitistic Dimension Conjectures for representations of quivers

Estrada S., ÖZDEMİR S.

TURKISH JOURNAL OF MATHEMATICS, vol.37, no.4, pp.585-591, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 4
  • Publication Date: 2013
  • Doi Number: 10.3906/mat-1106-13
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.585-591
  • Keywords: Finitistic dimension conjecture, path ring, quasi-Frobenius ring, quiver representation, ALGEBRAS
  • Dokuz Eylül University Affiliated: Yes

Abstract

Let R be a ring and Q be a quiver. We prove the first Finitistic Dimension Conjecture to be true for RQ, the path ring of Q over R, provided that R satisfies the conjecture. In fact, we prove that if the little and the big finitistic dimensions of R coincide and equal n < infinity, then this is also true for RQ and, both the little and the big finitistic dimensions of RQ equal n + 1 when Q is non-discrete and n when Q is discrete. We also prove that RQ is a quasi-Frobenius ring if and only if R is quasi-Frobenius and Q is discrete.