数学研究通讯

2018, (01) 23-35

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Extensions of Modules with ACC on d-annihilators

Ouyang Lun-qun;Zhou Qiong;Liu Jin-wang;Xiang Yue-ming;

摘要(Abstract):

A unitary right R-module MR satisfies acc on d-annihilators if for every sequence(a_n)_n of elements of R the ascending chain AnnM(a_1)■ AnnM(a_1 a_2)■AnnM(a_1 a_2 a_3)■… of submodules of MR stabilizes. In this paper we first investigate some triangular matrix extensions of modules with acc on d-annihilators. Then we show that under some additional conditions,the Ore extension module M[x]R[x;α,δ]over the Ore extension ring R[x;α,δ] satisfies acc on d-annihilators if and only if the module MR satisfies acc on d-annihilators. Consequently, several known results regarding modules with acc on d-annihilators are extended to a more general setting.

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作者(Author): Ouyang Lun-qun;Zhou Qiong;Liu Jin-wang;Xiang Yue-ming;

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