152
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Representation dimension of generalized path algebras of cyclic quivers

Pages 2296-2305 | Received 12 May 2015, Published online: 07 Oct 2016

References

  • Asadollahi, J., Eshraghi, H., Hafezi, R., Salarian, Sh. (2011). On the homotopy categories of projective and injective representations of quivers. J. Algebra 346(1):101–115.
  • Assem, I., Platzek, M. I., Trepode, S. (2006). On the representation dimension of tilted and laura algebras. J. Algebra 296:426–439.
  • Auslander, M. (1999). The Representation Dimension of Artin Algebras. Queen Mary College Mathematics Notes (1971). Republished in Selected works of Maurice Auslander. Providence: American Mathematical Society.
  • Auslander, M., Reiten, I., Smalø, S. O. (1995). Representation Theory of Artin Algebras. In: Cambridge Studies in Advanced Mathematics, Vol. 36. Cambridge: Cambridge University Press, xiv+423 pp.
  • Coelho, F., Platzeck, M. I. (2004). On the representation dimension of some classes of algebras. J. Algebra 275:615–628.
  • Enochs, E., Estrada, S. (2005). Projective representations of quivers. Commun. Algebra 33:3467–3478.
  • Enochs, E., Estrada, S., García Rozas, J. R. (2009). Injective representations of infinite quivers. Appl. Canad. J. Math. 61(2):315–335.
  • Enochs, E., Estrada, S., García Rozas, J. R., Iacob, A. (2007). Gorenstein quivers. Arch. Math. (Basel) 88(3):199–206.
  • Enochs, E., Estrada, S., Özdemir, S. (2013). Transfinite tree quivers and their representations. Math. Scand. 112(1):49–60.
  • Enochs, E., García Rozas, J. R., Oyonarte, L., Park, S. (2002). Noetherian quivers. Quaest. Math. 25(4):531–538.
  • Enochs, E., Herzog, I. (1999). A homotopy of quiver morphisms with applications to representations. Canad. J. Math. 51(2):294–308.
  • Enochs, E., Oyonarte, L., Torrecillas, B. (2004). Flat covers and flat representations of quivers. Commun. Algebra 32(4):1319–1338.
  • Eshraghi, H. (2014). The Auslander-Reiten translation in morphism categories. J. Algebra Appl. 13(3):1350119.
  • Gabriel, P. (1972). Unzerlegbare darstellungen I. Manuscripta Math. 6:71–103.
  • Igusa, K., Todorov, G. (2005). On the finitistic global dimension conjecture for Artin algebras. Fields Inst. Commun. 45:201–204.
  • Iyama, O. (2003). Finiteness of representation dimension. Proc. Am. Math. Soc. 131:1011–1014.
  • Luo, X.-H., Zhang, P. (2013). Monic representations and Gorenstein-projective modules. Pac. J. Math. 264(1): 163–194.
  • Mitchel, B. (1972). Rings with several objects. Adv. Math. 8:1–161.
  • Oppermann, S. (2009). Wild algebras have one-point extensions of representation dimension at least four. J. Pure Appl. Algebra 213(10):1945–1960.
  • Oppermann, S. (2010). Representation dimension of quasi-tilted algebras. J. Lond. Math. Soc. 2(81):435–456.
  • Ringel, C. M. (2012). On the representation dimension of artin algebras. Bull. Inst. Math. Acad. Sin. (N.S.) 7(1):33–70.
  • Rouquier, R. (2006). Representation dimension of exterior algebras. Inventiones Math. 165:357–367.
  • Rump, W. (2013). Injective tree representations. J. Pure Appl. Algebra 217(1):132–136.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.