We characterize V modules by relative (quasi )continuity of left R modules in this paper. It is shown that a left R module M is a V module if and only if every finitely cogenerated left R ...We characterize V modules by relative (quasi )continuity of left R modules in this paper. It is shown that a left R module M is a V module if and only if every finitely cogenerated left R module in σ[M] is S ( quasi )continuous if and only if every left R module in σ[M] is S continuous, where S is the set of all simple left R modules. We also show that a left R module M is a locally noetherian V module if and only if every semisimple left R module (in σ[M]) is M injective if and only if every essential extension in σ[M] of every semisimple left R module in σ[M] is S ? 2 (quasi )continuous, where S ? 2 is the set of all semisimple left R modules.展开更多
文摘We characterize V modules by relative (quasi )continuity of left R modules in this paper. It is shown that a left R module M is a V module if and only if every finitely cogenerated left R module in σ[M] is S ( quasi )continuous if and only if every left R module in σ[M] is S continuous, where S is the set of all simple left R modules. We also show that a left R module M is a locally noetherian V module if and only if every semisimple left R module (in σ[M]) is M injective if and only if every essential extension in σ[M] of every semisimple left R module in σ[M] is S ? 2 (quasi )continuous, where S ? 2 is the set of all semisimple left R modules.
