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《Journal of Anhui Normal University(Natural Science)》 1989-01
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QUASI—INJ., QUASI—PROJ., QUASI—FLAT Module and Special Rings

Chen Jianlong(Department of Mathematics)  
In this paper, we describe right (q)IF ring; left coherent ring; left coherent right perfect; left noether; left artin ring and regular ring in term of quasiinjective, quasi-projective, quasi-flat and character modules. Some of results are. Th3.5 f.a.e.(1) R is left coherent ring; (2) every (fp)-injective _RM, M~+ is quasi-flat; (3) every flat(free) M_R, M~(++) is quasi-flat. Th 3.8 f.a.e.(1) R is left coherent right perfect ring; (2) every (fp)-injective _RM, M~+ is quasi-proj; (3) every flat(free)MR, M~(++) is quasi-proj. Th 3.10 R is left noether ring iff "_RM is ∏-quasi-inj.(?)M~+ is quasi-flat". Th 3.11 R is left artin ring iff"_RM is(∏)-quasi-inj, (?)M~+ is quasi-proj."
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