i-单内射半模

i-Simple Injective Semimodules

作为单内射半模和i-内射半模的共同推广,给出了i-单内射半模的定义,讨论了i-单内射半模与Hom函子的关系,证明了单内射半模与i-内射半模的大部分性质对于i-单内射半模依然成立,同时给出了i-单内射半模的其它性质。

As a generalization of simple injective semimodules and i-injective semimodules,the concept of i-simple injective semimodule was introduced. The relationship between i-simple simple injecrive semimodules and Horn （ - ,N） was proved based on the notion. Several results of simple injecrive semimodules and i-injective semimodules also hold for i-simple injective semimodules. Some characterizations and properties of i-simple injective semimodules were given.