t-extending模的直和

Direct sums of t-extending modules

提出了t-补子模的概念,它与t-闭子模是等价的。讨论了t-extending模的直和因子的内射性,研究了t-extending模的直和,证明了M=i∈I M_(i)(|I|≥2)是t-extending模的等价条件有以下两个:(1)存在i≠j∈I,使得对M的任意t-闭子模K,若K∩M_(i)≤Z_(2)(M)或K∩M_(j)≤Z_(2)(M),则K是M的直和因子;(2)存在i≠j∈I,使得M_(j)或M_(i)在M中的任意t-补是t-extending模且是M的直和因子。

The concept of t-complement submodule was introduced,and it was equivalent to t-closed submodule.The injectivity of direct summand of t-extendingmodule was discussed,and the direct sums of t-extending module was studied.It was proved that there are two equivalent characterizations which M=i∈IM_(i)(|I|≥2)is t-extending modules:(1)There exist i≠j in I such that every t-closed submodule K of M with K∩M_(i)≤Z_(2)(M)or K∩M_(j)≤Z 2(M)is a direct summand;(2)There exist i≠j in I such that every t-complement of M_(i) or M_(j) in M is a t-extending module and a direct summand of M.