以下为句子列表：
英文: For every χsubmodule N of M,there exists a direct summand K of M,such that K∩N=0,and KN is an essential submodule of M;
中文: 对于模 M的任意一个χ-子模 N,存在模 K|M,使得 K∩ N =0 ,且 K N≤ e M;
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英文: For every χesubmodule N of M,there exists a direct summand K of M,such that K∩N=0,and KN is an essential submodule of M;
中文: 对于模 M的任意一个χe-子模 N,存在模 K|M,使得 K∩ N =0 ,且 K N≤ e M;
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英文: As a generalization of FI-C-modules,a concept of strong FI-C-modules(every fully invariant submodule of M has a fully invariant complement as a direct summand of M) was introduced,and its basic properties were discussed.
中文: 作为FI-C-模的推广,引入强FI-C-模(如果M的任意全不变子模存在一个全不变的补子模是M的直和因子),讨论该模的基本性质.
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英文: For example,it is proved that the direct sum M=_i∈IM_i is lifting if and only if there exists i∈I such that very coclosed submodule K of M with M=K+M_-i is a direct summand,or every supplement P of M_i in M is a direct summand and M/P is lifting.
中文: 例如证明了M=i∈IMi是提升模当且仅当存在i∈I,对M的任意余闭子模K,若M=K+M-i,则K是M的直和项,或者Mi在M中的任意补P是M的直和项且M/P是提升模.
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英文: module M is a direct injective module for each monomorphism f: N→A(N is a direct summand of M,A is any submodule of M and),and the mapping Hom(f, M):Hom(A,M)→Hom( N,M) surjective; if is a direct injective module, then Mα so is Mα.
中文: 模M为直内射模对每个单同态f：N→A（N为M的直和顶，A为M的包含N的任意子模）有Hom（f，M）：Hom（A，M）→Hom（N，M）是满同态。
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