关于fann-内射模

On Fann-injective Modules

讨论了fann-内射模的等价刻画和基本性质,证明了i∈ΛMi是fann-内射左R-模当且仅当每一Mi是fann-内射左R-模;若环R的每个有限生成闭左理想都是投射左R-模,则fann-内射左R-模的商模是fann-内射左R-模.同时讨论了一类特殊的fann-内射模——fann-自内射环的等价刻画及特性,证明了在左fann-自内射环里若左零化子理想l(I)是有限生成的,则Rδ/I是满射.最后讨论了fann-自内射环的零化子条件以及理想的自反性,证明了左fann-自内射环的有限生成理想l(I)是自反模.

In this paper, the equivalent characterizations and properties of fann-injective module are studied. Especially it is proved that i∈ Mi is a fann-injective module if and only if for each i ∈A ,Mi is a fann-injective module ; if every finitely generated closed left ideal is a projective left R-module, the quotient module of the fann-injective left R-module is a fann-injective left R-module. At the same time, the equivalent characterizations and properties of the fann-injective ring are also discussed. It is brought out that if the left annihilator l（I） is finitely generated in the left fann-injective rings, the δR/1 is surjective. Finally the annihilator conditions and the reflexive properties of the ideals are studied in fann-injective ring. For example, every finitely generated ideal l（1） of the fann-injective ring is a reflexive module.