A commutative ring R is said to be endo-Noetherian if the chain of annihilators \({ ann}(a_{1})\subseteq \)\({ ann}(a_{2})\subseteq \cdots \) stabilizes for each sequence \((a_{k})_{k}\) of elements of R (Ndiaye and Gueye in Int J Appl Math 86:871–881, 2013). In this paper, we give equivalent conditions for the power series (resp., polynomial) rings over an Armendariz ring to be endo-Noetherian. We also study several properties of an endo-Noetherian ring. The concept of the amalgamated duplication of R along an ideal \(I, R\bowtie I\) is studied.

中文翻译：

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内-诺醚环

交换环- [R被认为是内切诺特如果零化子的链\（{安}（A_ {1}）\ subseteq \）\（{安}（A_ {2}）\ subseteq \ cdots \）稳定为R元素的每个序列\（（（a_ {k}）_ {k} \）（India J Appl Math 86：871–881，2013）中的Ndiaye和Gueye。在本文中，我们为Armendariz环上的幂级数环（分别是多项式）给出了等价的条件，即为内Noether环。我们还研究了内诺醚环的几种性质。研究了沿着理想\（I，R \ bowtie I \）合并R的概念。