TY  - JOUR
T1  - Abelian model structures and Ding homological dimensions
AU  - Wei, Chongqing
AU  - Wang, Limin
AU  - Liu, Zhongkui
PY  - 2016
DA  - October
JF  - Hacettepe Journal of Mathematics and Statistics
PB  - Hacettepe University
WT  - DergiPark
SN  - 2651-477X
SP  - 1461
EP  - 1474
VL  - 45
IS  - 5
LA  - en
AB  - Let $R$ be an $n$-FC ring. For $0<t\leq n$, we construct a new abelian model structure on $R$-Mod, called the Ding $t$-projective ($t$-injective) model structure. Based on this, we establish a bijective correspondence between $dg$-$t$-projective ($dg$-$t$-injective) $R$-complexes and Ding $t$-projective ($t$-injective) $A$-modules under some additional conditions, where $A=R[x]/(x^2)$. This gives a generalized version of the bijective correspondence established in [14] between $dg$-projective ($dg$-injective) $R$-complexes and Gorenstein projective (injective) $A$-modules. Finally, we show that the embedding functors $K(\mathcal{D} \mathcal{P})\rightarrow K$ ($R$-Mod) and $K(\mathcal{D} \mathcal{J})\rightarrow K$ ($R$-Mod) have right and left adjoints respectively, where $K(\mathcal{D} \mathcal{P})$ ($K(\mathcal{D} \mathcal{J})$) is the homotopy category of complexes of Ding projective (injective) modules, and $K$ ($R$-Mod) denotes the homotopy category. 
KW  - model structures
KW  - Ding $t$-projective (injective) modules
KW  - $dg$-$t$-projective (injective) complexes
KW  - adjoint functors
CR  - [14] Gillespie J., Hovey M.: Gorenstein model structures and generalized derived categories. Submitted to Proceedings of the Edinburgh Mathematical Society.
UR  - https://dergipark.org.tr/en/pub/hujms/issue//524474
L1  - https://dergipark.org.tr/en/download/article-file/644878
ER  -