Finitistic Dimension Conjectures for representations of quivers

Estrada S., ÖZDEMİR S.

TURKISH JOURNAL OF MATHEMATICS, cilt.37, sa.4, ss.585-591, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 37 Sayı: 4
  • Basım Tarihi: 2013
  • Doi Numarası: 10.3906/mat-1106-13
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.585-591
  • Anahtar Kelimeler: Finitistic dimension conjecture, path ring, quasi-Frobenius ring, quiver representation, ALGEBRAS
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

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.