Locally κ-presented representation of quiver

Document Type : Research Paper

Author

Department of Pure Mathematics Faculty of Mathematical Sciences, University of Guilan P. O. Box 41335-19141, Rasht, Iran

Abstract

In this paper, we focus on the concept of locally κ-presented representations of quiver and we introduce two classes of objects of representations of the quiver on certain Grothendieck category related to this concept which forms a complete cotorsion pair.

Keywords


1. L. Bican, R. El. Bashir and E. Enochs, All modules have  at covers, Bull. London Math. Soc, 33(4) (2001), 385-390.
2. E. Enochs, S. Estrada and I. Iacob, Cotorsion pairs, model structures and adjoints in homotopy categories, Houston J. Math. (1) 40 (2014), 43-61.
3. H. Eshraghi, R. Hafezi, E. Hosseini and Sh. Salarian, Cotorsion theory in the category of quiver representations, J. Algebra Appl, (6) 12 (2013), http://doi.org/10.1142/S0219498813500059.
4. P.C. Eklof, Homological algebra and set theory, Trans. Amer. Math. Soc. 227(1977), 207-225.
5. L.Fuchs and S. B. Lee, From a single chain to a large family of submodules, Port.Math. (N.S.) 61 (2004), 193-205.
6. P. Hill, The third axiom of countability for abelian groups, Proc. Amer. Math. Soc., (3) 82 (1981) 347-350.
7. H. Holm and P. Jrgensen, Cotorsion pairs in categories of quiver representations, Kyoto J. Math. (3) 59 (2019), 575-606.
8. M. Hovey, Cotorsion pair, model category structures, and representation theory, Math. Zeit. 241 (2002), 553-592.
9. B. Mitchell, On the dimension of objects and categories. II. Finite ordered sets, J. Algebra, 9 (1968), 341-368.
10. W. Rump, Injective tree representations, J. Pure Appl. Algebra, 217 (2013),132-136.
11. L. Salce, Cotorsion theory for abelian groups, Symposia Math. 23, 11-32, Academic Press, New York, 1979.
12. J. Stovcek, Deconstructibility and Hill lemma in Grothendieck categories, Forum Math. 25 (2013), 193-219.