Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

ABSOLUTELY PURE REPRESENTATIONS OF QUIVERS

  • Aghasi, Mansour (Department of Mathematical sciences Isfahan University of Technology) ;
  • Nemati, Hamidreza (Department of Mathematical sciences Isfahan University of Technology)
  • Received : 2013.12.16
  • Published : 2014.11.01
Download PDF
⟨ Previous Next ⟩

Abstract

In the current paper we study absolutely pure representations of quivers. Then over some nice quivers including linear quivers some sufficient conditions guaranteeing a representation to be absolutely pure is characterized. Furthermore some relations between atness and absolute purity is investigated. Finally it is shown that the absolutely pure covering of representations of linear quivers (including $A^-_{\infty}$, $A^+_{\infty}$ and $A^{\infty}_{\infty}$) by R-modules whenever R is a coherent ring exists.

Keywords

References

  1. D. D. Adams, Absolutely pure modules, Ph.D. Thesis, University of Kentucky, Department of Mathematics, 1978.
  2. E. Enochs, Shortening filtrations, Sci. China Math. 55 (2012), no. 4, 687-693. https://doi.org/10.1007/s11425-011-4334-2
  3. E. Enochs and S. Estrada, Projective representations of quivers, Comm. Algebra 33 (2005), no. 10, 3467-3478. https://doi.org/10.1081/AGB-200058181
  4. E. Enochs and S. Estrada, Relative homological algebra in the category of quasi-coherent sheaves, Adv. Math. 194 (2005), no. 2, 284-295. https://doi.org/10.1016/j.aim.2004.06.007
  5. E. Enochs, S. Estrada, and G. Rozas, Injective representations of in nite quivers. applications, Canad. J. Math. 61 (2009), no. 2, 315-335. https://doi.org/10.4153/CJM-2009-016-2
  6. E. Enochs, L. Oyonarte, and B. Torrecillas, Flat covers and flat representations of quivers, Comm. Algebra 32 (2004), no. 4, 1319-1338. https://doi.org/10.1081/AGB-120028784
  7. S. Estrada and S. Ozdemir, Relative homological algebra in categories of representation of quivers, Houston J. Math. 39 (2013), no. 2, 343-362.
  8. E. Hosseini, Pure injective representations of quivers, Bull. Korean Math. Soc. 50 (2013), no. 2, 389-398. https://doi.org/10.4134/BKMS.2013.50.2.389
  9. B. H. Maddox, Absolutely pure modules, Proc. Amer. Math. Soc. 18 (1967), no. 1, 155-158. https://doi.org/10.1090/S0002-9939-1967-0224649-5
  10. C. Megibben, Absolutely pure modules, Proc. Amer. Math. Soc. 26 (1970), no. 4, 561-566. https://doi.org/10.1090/S0002-9939-1970-0294409-8
  11. S. Park, Injective and projective properties of representations of quivers with n edges, Korean J Math. 16 (2008), no. 3, 323-334.
  12. K. Pinzon, Absolutely pure covers, Comm. Algebra 36 (2008), no. 6, 2186-2194. https://doi.org/10.1080/00927870801952694
  13. B. Stenstrom, Coherent rings and Fp-injective modules, J. London Math. Soc. 2 (1970), 323-329.