Abstract:In this paper, we study approximations of modules in that class by modules which are either Ding injective or else have finite injective dimension. We construct two adjoint functors of the stable categories of Ding injective R-modules.
[1] EMMANOUIL I, TALELLI O. Finiteness criteria in gorenstein homological algebra[J]. Transactions of the American Mathematical Society,2014, 366(12):6329-6351.
[2] MAO L X, DING N Q. Gorenstein FP-injective and gorenstein flat modules[J]. Journal of Algebra & Its Applications, 2008, 7(4):491-506.
[3] GILLESPIE J. Model structures on modules over Ding-Chen rings[J]. Homology, Homotopy & Applications,2010, 12(1):61-73.
[4] STENSTRÖM B. Coherent rings and FP-injective modules[J]. Journal of the London Mathematical Society, 1970, 2(2):323-329.
[5] YANG G, LIU Z K, LIANG L. Ding-projective and Ding-injective modules[J]. Algebra Colloquium, 2013, 20(4):601-612.
[6] HUANG C L, WU T S. Ding-projective and Ding-injective dimensions[J]. International Electornic Journal of Algebra, 2015, 18:1-20.