摘要
本文利用拟内射、拟投射、拟平坦和特征模刻划了如下一些特殊环:右(q)IF环;左Coherent环;左Coherent右完全环;左ncether环;左Artin环和正则环。
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.'
关键词
拟内射
拟投射
拟平坦
特殊环
quasi-injective, quasi-projective, quasi-flat, left coherent ring.
