Finitistic Dimension Conjectures for representations of quivers
TURKISH JOURNAL OF MATHEMATICS, cilt.37, sa.4, ss.585-591, 2013 (SCI-Expanded, Scopus, TRDizin)
- 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
- 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.