直和补模和H-补模(英文)

⊕-SUPPLEMENTED MODULES AND H-SUPPLEMENTED MODULES

模M称为直和补的是指M的任何一个子模都有一个是直和项的加补.模M称为H-补的是指,对M的任何一个子模A,都存在一个直和项L,使得A+X=M成立当且仅当M=L+X.本文主要给出了直和补模和H-补模的一些性质刻画.并证明了任何一个直和补模,如果其自同态环H满足Id(H)=S_l(H),则它有一个不可分的分解.

Let M be a module.M is⊕-supplemented if every submodule of M has a supplement that is a direct summand.M is called an H-supplemented module if for a submodule A of M,there exists a direct summand D of M such that A+ X=M holds if and only if M=D+X.In this paper,we obtain some properties, characterizations of⊕-supplemented modules and H-supplemented modules.We also proved that every⊕-supplemented module M with Id(H)=S_l(H) where H=End(M) has an indecomposable decomposition.