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A new characterization of cyclic modules over local rings
Journal of Algebra and Its Applications ( IF 0.5 ) Pub Date : 2021-03-18 , DOI: 10.1142/s0219498822501304
Reza Naghipour 1
Affiliation  

The aim of this paper is to give a new characterization of cyclic modules over local rings, namely, we show that if N is a nonzero finitely generated module over a local (Noetherian) ring (R,𝔪) such that for some integer n1, the submodule 𝔪nN of N is cyclic, then every submodule of N is cyclic and the ring R/AnnR(N) is a DVR, whenever depthN>0. As a consequence, it follows that R/AnnR(N/Γ𝔪(N)) is a DVR and every submodule of N/Γ𝔪(N) is cyclic.



中文翻译:

局部环上循环模的新表征

本文的目的是给出局部环上循环模块的新特征,即,我们证明如果ñ是局部(Noetherian)环上的非零有限生成模块(R,𝔪)这样对于某个整数n1, 子模块𝔪nññ是循环的,那么每个子模ñ是循环的并且环R/R(ñ)是一个DR, 每当深度ñ>0. 其结果是,R/R(ñ/Γ𝔪(ñ))是一个DR和每个子模块ñ/Γ𝔪(ñ)是循环的。

更新日期:2021-03-18
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