Let C be a class of R-modules closed under isomorphisms and finite direct sums. It is first shown that the finite direct sum of almost C-precovers is an almost C-precover and the direct sum of an almost C-cover and a ...Let C be a class of R-modules closed under isomorphisms and finite direct sums. It is first shown that the finite direct sum of almost C-precovers is an almost C-precover and the direct sum of an almost C-cover and a weak C-cover is a weak C-cover. Then the notion of almost C-preenvelopes is introduced and studied.展开更多
An R-module M is called Gorenstein FP-injective if there is an exact sequence …→E1→E0→E^0→E^1→… of FP-injective R-modules with M=ker（E^0→E^1） and such that Hom（E,-） leaves the sequence exact whenever E is ...An R-module M is called Gorenstein FP-injective if there is an exact sequence …→E1→E0→E^0→E^1→… of FP-injective R-modules with M=ker（E^0→E^1） and such that Hom（E,-） leaves the sequence exact whenever E is an FP-injective R-module.Some properties of Gorenstein FP-injective are obtained.Moreover,it is proved that a ring is left Noetherian if and only if every Gorenstein FP-injective left R-module is Gorenstein injective.Furthermore,it is shown that over an n-FC and perfect ring R,a left R-module M is Gorenstein FP-injective if and only if MFH for some FP-injective left R-module F and some strongly Gorenstein FP-injective R-module H.In view of this,Gorenstein FP-injective precovers and Gorenstein FP-injective preenvelopes are considered.展开更多
基金This research was partially supported by the Specialized Research Fund for the Doctoral Program of Higher ducation of China (20020284009, 20030284033) NSF of China (10331030) Jiangsu Planned Projects for Postdoctoral Research Funds (0203003403)the Postdoctoral Research Funds of China (2006037713)and the Nanjing Institute of Technology of China.
文摘Let C be a class of R-modules closed under isomorphisms and finite direct sums. It is first shown that the finite direct sum of almost C-precovers is an almost C-precover and the direct sum of an almost C-cover and a weak C-cover is a weak C-cover. Then the notion of almost C-preenvelopes is introduced and studied.
基金The National Natural Science Foundation of China (No.10971024)Specialized Research Fund for the Doctoral Program of Higher Education (No. 200802860024)
文摘An R-module M is called Gorenstein FP-injective if there is an exact sequence …→E1→E0→E^0→E^1→… of FP-injective R-modules with M=ker（E^0→E^1） and such that Hom（E,-） leaves the sequence exact whenever E is an FP-injective R-module.Some properties of Gorenstein FP-injective are obtained.Moreover,it is proved that a ring is left Noetherian if and only if every Gorenstein FP-injective left R-module is Gorenstein injective.Furthermore,it is shown that over an n-FC and perfect ring R,a left R-module M is Gorenstein FP-injective if and only if MFH for some FP-injective left R-module F and some strongly Gorenstein FP-injective R-module H.In view of this,Gorenstein FP-injective precovers and Gorenstein FP-injective preenvelopes are considered.
