$\mathcal{X}$-injective and $\mathcal{X}$-projective complexes

Document Type : Research Paper


Department of Mathematics‎, ‎Abant Izzet Baysal University‎, Gölköy Kampüsü Bolu, Turkey.


Let $\mathcal{X}$ be a class of $R$-modules‎. ‎In this paper‎, ‎we investigate \;$\mathcal{X}$-injective (projective) and DG-$\mathcal{X}$-injective (projective) complexes which are generalizations of injective (projective) and DG-injecti‎‎ve (projective) complexes‎. ‎We prove that some known results can be extended to the class of \;$\mathcal{X}$-injective (projective) and DG-$\mathcal{X}$-injective (projective) complexes for this general settings.


Main Subjects

L. L. Avramov and H. B. Foxby, Homological dimensions of unbounded complexes, J. Pure Appl. Algebra 71 (1991), no. 2-3, 129--155.
E. E. Enochs, O. M. G. Jenda and J. Xu, Orthogonality in the category of complexes, Math. J. Okayama Univ. 38 (1996) 25--46.
E. E. Enochs and O. M. G. Jenda, Relative Homological Algebra, de Gruyter Ex. Math., 30, Walter de Gruyter & Co., Berlin, 2000.
P. Eklof, Homological algebra and set theory, Trans. Amer. Math. Soc. 227 (1977) 207--225.
J. Gillespie, The at model structure on Ch(R), Trans. Amer. Math. Soc. 356 (2004), no. 8, 3369--3390.
L. X. Mao and N. Q. Ding, L-injective hulls of modules, Bull. Aust. Math. Soc. 74 (2006), no. 1, 37--44.
Joseph J. Rotman, An Introduction to Homological Algebra, Springer, New York, 2009.
J. T. Stafford and R. B. Wareld, Construction of Hereditary Noetherian Rings, Proc. Lond. Math. Soc. (3) 51 (1985), no. 1, 1--20.
J. Trlifaj, Ext and inverse limits, Illinois J. Math. 47 (2003), no. 1-2, 529--538.